Here's another option. I have slightly modified your code, so substitute yours with this one:
\makeatletter
\renewcommand*{\makecvtitle}{%
% recompute lengths (in case we are switching from letter to resume, or vice versa)
\recomputecvlengths%
% optional detailed information (pre-rendering)
\def\phonesdetails{}%
\collectionloop{phones}{% the key holds the phone type (=symbol command prefix), the item holds the number
\protected@edef\phonesdetails{\phonesdetails\protect\makenewline\csname\collectionloopkey phonesymbol\endcsname\collectionloopitem}}%
\def\socialsdetails{}%
\collectionloop{socials}{% the key holds the social type (=symbol command prefix), the item holds the link
\protected@edef\socialsdetails{\socialsdetails\protect\makenewline\csname\collectionloopkey socialsymbol\endcsname\collectionloopitem}}%
\newbox{\makecvtitledetailsbox}%
\savebox{\makecvtitledetailsbox}{%
\addressfont\color{color2}%
\begin{tabular}[b]{@{}l@{}}%
\makenewline
\ifthenelse{\isundefined{\@addressstreet}}{}{\makenewline\addresssymbol\@addressstreet%
\ifthenelse{\equal{\@addresscity}{}}{}{\makenewline\@addresscity}% if \addresstreet is defined, \addresscity and addresscountry will always be defined but could be empty
\ifthenelse{\equal{\@addresscountry}{}}{}{\makenewline\@addresscountry}}%
\phonesdetails% needs to be pre-rendered as loops and tabulars seem to conflict
\ifthenelse{\isundefined{\@email}}{}{\makenewline\emailsymbol\emaillink{\@email}}%
\ifthenelse{\isundefined{\@homepage}}{}{\makenewline\homepagesymbol\httplink{\@homepage}}%
\socialsdetails% needs to be pre-rendered as loops and tabulars seem to conflict
\ifthenelse{\isundefined{\@extrainfo}}{}{\makenewline\@extrainfo}%
\end{tabular}}%
% optional photo (pre-rendering)
\newbox{\makecvtitlepicturebox}%
\savebox{\makecvtitlepicturebox}{%
\ifthenelse{\isundefined{\@photo}}%
{
\@initializelength{\makecvtitlepicturewidth}% Damit Länge bekannt bei Name
\settowidth{\makecvtitlepicturewidth}{0pt}%
}%
{%
\setlength\fboxrule{\@photoframewidth}%
\ifdim\@photoframewidth=0pt%
\setlength{\fboxsep}{0pt}\fi%
{\color{color1}\framebox{\includegraphics[width=\@photowidth]{\@photo}}}}
\@initializelength{\makecvtitlepicturewidth}%
\settowidth{\makecvtitlepicturewidth}{\usebox{\makecvtitlepicturebox}}%
}%
% end define optional picture
% optional detailed information (rendering)
% name
% \parbox[b]{\textwidth-\makecvtitlepicturewidth}{%
{\raggedright\namefont{\color{color2!50}\@firstname} {\color{color2}\@familyname}}\\[1em]
\usebox{\makecvtitledetailsbox}% \llap is used to suppress the width of the box, allowing overlap if the value of
\hfill\usebox{\makecvtitlepicturebox}%
% \parbox[b]{\textwidth-\makecvtitlepicturewidth}{%
% \raggedleft\namefont{\color{color2!50}\@firstname} {\color{color2}\@lastname}}%\familyname
\\[-.35em]%
{\color{color2!50}\rule{\textwidth}{.25ex}}%
% optional title
% { \raggedright\namefont{\color{color2!50}\@firstname} {\color{color2}\@familyname}}
\ifthenelse{\equal{\@title}{}}{}{\\[1.25em]\null\hfill\titlestyle{\@title}}\\[2.5em]%
% optional quote
\ifthenelse{\isundefined{\@quote}}%
{}%
{{\null\hfill\begin{minipage}{\quotewidth}\centering\quotestyle{\@quote}\end{minipage}\hfill\null\\[2.5em]}}%
\par}%
\makeatother
This is the result
inserting that code in a MWE:
\documentclass[11pt,a4paper,sans]{moderncv} % possible options include font size ('10pt', '11pt' and '12pt'), paper size ('a4paper', 'letterpaper', 'a5paper', 'legalpaper', 'executivepaper' and 'landscape') and font family ('sans' and 'roman')
% moderncv themes
\moderncvstyle{classic} % style options are 'casual' (default), 'classic', 'oldstyle' and 'banking'
\moderncvcolor{blue} % color options 'blue' (default), 'orange', 'green', 'red', 'purple', 'grey' and 'black'
%\renewcommand{\familydefault}{\sfdefault} % to set the default font; use '\sfdefault' for the default sans serif font, '\rmdefault' for the default roman one, or any tex font name
%\nopagenumbers{} % uncomment to suppress automatic page numbering for CVs longer than one page
% character encoding
%\usepackage[utf8]{inputenc} % if you are not using xelatex ou lualatex, replace by the encoding you are using
%\usepackage{CJKutf8} % if you need to use CJK to typeset your resume in Chinese, Japanese or Korean
% adjust the page margins
\usepackage[scale=0.75]{geometry}
%\setlength{\hintscolumnwidth}{3cm} % if you want to change the width of the column with the dates
%\setlength{\makecvtitlenamewidth}{10cm} % for the 'classic' style, if you want to force the width allocated to your name and avoid line breaks. be careful though, the length is normally calculated to avoid any overlap with your personal info; use this at your own typographical risks...
% personal data
\name{John}{Doe}
\title{Curriculum Vitae} % optional, remove / comment the line if not wanted
\address{street and number}{postcode city}{country}% optional, remove / comment the line if not wanted; the "postcode city" and "country" arguments can be omitted or provided empty
\phone[mobile]{+1~(234)~567~890} % optional, remove / comment the line if not wanted; the optional "type" of the phone can be "mobile" (default), "fixed" or "fax"
\phone[fixed]{+2~(345)~678~901}
\phone[fax]{+3~(456)~789~012}
\email{[email protected]} % optional, remove / comment the line if not wanted
\homepage{www.johndoe.com} % optional, remove / comment the line if not wanted
\social[linkedin]{john.doe} % optional, remove / comment the line if not wanted
\social[twitter]{jdoe} % optional, remove / comment the line if not wanted
\social[github]{jdoe} % optional, remove / comment the line if not wanted
\extrainfo{additional information} % optional, remove / comment the line if not wanted
\photo[64pt][0.4pt]{picture} % optional, remove / comment the line if not wanted; '64pt' is the height the picture must be resized to, 0.4pt is the thickness of the frame around it (put it to 0pt for no frame) and 'picture' is the name of the picture file
\quote{Some quote} % optional, remove / comment the line if not wanted
% to show numerical labels in the bibliography (default is to show no labels); only useful if you make citations in your resume
%\makeatletter
%\renewcommand*{\bibliographyitemlabel}{\@biblabel{\arabic{enumiv}}}
%\makeatother
%\renewcommand*{\bibliographyitemlabel}{[\arabic{enumiv}]}% CONSIDER REPLACING THE ABOVE BY THIS
% bibliography with mutiple entries
%\usepackage{multibib}
%\newcites{book,misc}{{Books},{Others}}
\makeatletter
\renewcommand*{\makecvtitle}{%
% recompute lengths (in case we are switching from letter to resume, or vice versa)
\recomputecvlengths%
% optional detailed information (pre-rendering)
\def\phonesdetails{}%
\collectionloop{phones}{% the key holds the phone type (=symbol command prefix), the item holds the number
\protected@edef\phonesdetails{\phonesdetails\protect\makenewline\csname\collectionloopkey phonesymbol\endcsname\collectionloopitem}}%
\def\socialsdetails{}%
\collectionloop{socials}{% the key holds the social type (=symbol command prefix), the item holds the link
\protected@edef\socialsdetails{\socialsdetails\protect\makenewline\csname\collectionloopkey socialsymbol\endcsname\collectionloopitem}}%
\newbox{\makecvtitledetailsbox}%
\savebox{\makecvtitledetailsbox}{%
\addressfont\color{color2}%
\begin{tabular}[b]{@{}l@{}}%
\makenewline
\ifthenelse{\isundefined{\@addressstreet}}{}{\makenewline\addresssymbol\@addressstreet%
\ifthenelse{\equal{\@addresscity}{}}{}{\makenewline\@addresscity}% if \addresstreet is defined, \addresscity and addresscountry will always be defined but could be empty
\ifthenelse{\equal{\@addresscountry}{}}{}{\makenewline\@addresscountry}}%
\phonesdetails% needs to be pre-rendered as loops and tabulars seem to conflict
\ifthenelse{\isundefined{\@email}}{}{\makenewline\emailsymbol\emaillink{\@email}}%
\ifthenelse{\isundefined{\@homepage}}{}{\makenewline\homepagesymbol\httplink{\@homepage}}%
\socialsdetails% needs to be pre-rendered as loops and tabulars seem to conflict
\ifthenelse{\isundefined{\@extrainfo}}{}{\makenewline\@extrainfo}%
\end{tabular}}%
% optional photo (pre-rendering)
\newbox{\makecvtitlepicturebox}%
\savebox{\makecvtitlepicturebox}{%
\ifthenelse{\isundefined{\@photo}}%
{
\@initializelength{\makecvtitlepicturewidth}% Damit Länge bekannt bei Name
\settowidth{\makecvtitlepicturewidth}{0pt}%
}%
{%
\setlength\fboxrule{\@photoframewidth}%
\ifdim\@photoframewidth=0pt%
\setlength{\fboxsep}{0pt}\fi%
{\color{color1}\framebox{\includegraphics[width=\@photowidth]{\@photo}}}}
\@initializelength{\makecvtitlepicturewidth}%
\settowidth{\makecvtitlepicturewidth}{\usebox{\makecvtitlepicturebox}}%
}%
% end define optional picture
% optional detailed information (rendering)
% name
% \parbox[b]{\textwidth-\makecvtitlepicturewidth}{%
{\raggedright\namefont{\color{color2!50}\@firstname} {\color{color2}\@familyname}}\\[1em]
\usebox{\makecvtitledetailsbox}% \llap is used to suppress the width of the box, allowing overlap if the value of
\hfill\usebox{\makecvtitlepicturebox}%
% \parbox[b]{\textwidth-\makecvtitlepicturewidth}{%
% \raggedleft\namefont{\color{color2!50}\@firstname} {\color{color2}\@lastname}}%\familyname
\\[-.35em]%
{\color{color2!50}\rule{\textwidth}{.25ex}}%
% optional title
% { \raggedright\namefont{\color{color2!50}\@firstname} {\color{color2}\@familyname}}
\ifthenelse{\equal{\@title}{}}{}{\\[1.25em]\null\hfill\titlestyle{\@title}}\\[2.5em]%
% optional quote
\ifthenelse{\isundefined{\@quote}}%
{}%
{{\null\hfill\begin{minipage}{\quotewidth}\centering\quotestyle{\@quote}\end{minipage}\hfill\null\\[2.5em]}}%
\par}%
\makeatother
%----------------------------------------------------------------------------------
% content
%----------------------------------------------------------------------------------
\begin{document}
%\begin{CJK*}{UTF8}{gbsn} % to typeset your resume in Chinese using CJK
%----- resume ---------------------------------------------------------
\makecvtitle
\section{Education}
\cventry{year--year}{Degree}{Institution}{City}{\textit{Grade}}{Description} % arguments 3 to 6 can be left empty
\cventry{year--year}{Degree}{Institution}{City}{\textit{Grade}}{Description}
\section{Master thesis}
\cvitem{title}{\emph{Title}}
\cvitem{supervisors}{Supervisors}
\cvitem{description}{Short thesis abstract}
\end{document}
EDIT (after your comments)
To have the photo top-aligned with the name, substitute the code between \makeatletter...\makeatother above with this one:
\makeatletter
\renewcommand*{\makecvtitle}{%
% recompute lengths (in case we are switching from letter to resume, or vice versa)
\recomputecvlengths%
% optional detailed information (pre-rendering)
\def\phonesdetails{}%
\collectionloop{phones}{% the key holds the phone type (=symbol command prefix), the item holds the number
\protected@edef\phonesdetails{\phonesdetails\protect\makenewline\csname\collectionloopkey phonesymbol\endcsname\collectionloopitem}}%
\def\socialsdetails{}%
\collectionloop{socials}{% the key holds the social type (=symbol command prefix), the item holds the link
\protected@edef\socialsdetails{\socialsdetails\protect\makenewline\csname\collectionloopkey socialsymbol\endcsname\collectionloopitem}}%
\newbox{\makecvtitledetailsbox}%
\savebox{\makecvtitledetailsbox}{%
\addressfont\color{color2}%
\begin{tabular}[b]{@{}l@{}}%
\makenewline
\ifthenelse{\isundefined{\@addressstreet}}{}{\makenewline\addresssymbol\@addressstreet%
\ifthenelse{\equal{\@addresscity}{}}{}{\makenewline\@addresscity}% if \addresstreet is defined, \addresscity and addresscountry will always be defined but could be empty
\ifthenelse{\equal{\@addresscountry}{}}{}{\makenewline\@addresscountry}}%
\phonesdetails% needs to be pre-rendered as loops and tabulars seem to conflict
\ifthenelse{\isundefined{\@email}}{}{\makenewline\emailsymbol\emaillink{\@email}}%
\ifthenelse{\isundefined{\@homepage}}{}{\makenewline\homepagesymbol\httplink{\@homepage}}%
\socialsdetails% needs to be pre-rendered as loops and tabulars seem to conflict
\ifthenelse{\isundefined{\@extrainfo}}{}{\makenewline\@extrainfo}%
\end{tabular}}%
% optional photo (pre-rendering)
\newbox{\makecvtitlepicturebox}%
\savebox{\makecvtitlepicturebox}{%
\ifthenelse{\isundefined{\@photo}}%
{}%
{%
\setlength\fboxrule{\@photoframewidth}%
\ifdim\@photoframewidth=0pt%
\setlength{\fboxsep}{0pt}\fi%
{\color{color1}\framebox{\includegraphics[width=\@photowidth]{\@photo}}}}
% \@initializelength{\makecvtitlepicturewidth}%
% \settowidth{\makecvtitlepicturewidth}{\usebox{\makecvtitlepicturebox}}%
}%
% end define optional picture
% optional detailed information (rendering)
% name
\newlength{\makecvtitledetailswidth}\settowidth{\makecvtitledetailswidth}{\usebox{\makecvtitledetailsbox}}%
\newlength{\makecvtitlepicturewidth}\settowidth{\makecvtitlepicturewidth}{\usebox{\makecvtitlepicturebox}}%
\ifthenelse{\lengthtest{\makecvtitlenamewidth=0pt}}% check for dummy value (equivalent to \ifdim\makecvtitlenamewidth=0pt)
{\setlength{\makecvtitlenamewidth}{\textwidth-\makecvtitledetailswidth-\makecvtitlepicturewidth}}%
{}%
\begin{minipage}[t]{\makecvtitlenamewidth}%
\vspace*{0pt}
\raggedright\namefont{\color{color2!50}\@firstname} {\color{color2}\@familyname}\\
\usebox{\makecvtitledetailsbox}% \llap is used to suppress the width of the box, allowing overlap if the value of
\end{minipage}%
\hfill%
\begin{minipage}[t]{\linewidth-\makecvtitlenamewidth}
\vspace*{0pt}%
\raggedleft\usebox{\makecvtitlepicturebox}%
\end{minipage}%
% \raggedleft\namefont{\color{color2!50}\@firstname} {\color{color2}\@lastname}}%\familyname
\\[.5em]%
{\color{color2!50}\rule{\textwidth}{.25ex}}%
% optional title
% { \raggedright\namefont{\color{color2!50}\@firstname} {\color{color2}\@familyname}}
\ifthenelse{\equal{\@title}{}}{}{\\[1.25em]\null\hfill\titlestyle{\@title}}\\[2.5em]%
% optional quote
\ifthenelse{\isundefined{\@quote}}%
{}%
{{\null\hfill\begin{minipage}{\quotewidth}\centering\quotestyle{\@quote}\end{minipage}\hfill\null\\[2.5em]}}%
\par}%
\makeatother
Output:
