Using one of the KOMA_Script document classes, the numbers=enddot
class option will use a full stop for the counters for sectional units, figures, tables. If you load the amsthm
package, counters for theorem-like structure will also have a full stop:
\documentclass[numbers=enddot]{scrartcl}
\usepackage{amsthm}
\newtheorem{theo}{Theorem}[section]
\begin{document}
\section{Test Section}
\subsection{Test Subsection}
\subsubsection{Test Subsubsection}
\begin{theo}
test
\end{theo}
\end{document}

Since you are using a custom theorem style, use the sixth mandatory argument of \newtheoremstyle
to add the necessary punctuation:
\usepackage{amsthm}
\newtheoremstyle{break}
{\topsep}{\topsep}%
{\itshape}{}%
{\bfseries}{.}%
{\newline}{}%
\theoremstyle{break}
\newtheorem{theo}{Theorem}[section]
To satisfy the requirement mentioned in a comment for the end dot position when the optional argument is used, some additional work will have to be done using the last mandatory argument for \newtheoremstyle
:
\documentclass[numbers=enddot]{scrartcl}
\usepackage{amsthm}
\newtheoremstyle{break}
{\topsep}{\topsep}%
{\itshape}{}%
{\bfseries}{}%
{\newline}{\thmname{#1}\thmnumber{ #2.}\thmnote{ \normalfont(#3)}}%
\theoremstyle{break}
\newtheorem{theo}{Theorem}[section]
\newtheoremstyle{breaknodot}
{\topsep}{\topsep}%
{\itshape}{}%
{\bfseries}{}%
{\newline}{\thmname{#1}\thmnote{ \normalfont(#3)}}%
\theoremstyle{breaknodot}
\newtheorem*{theo*}{Theorem}
\begin{document}
\section{Test Section}
\subsection{Test Subsection}
\subsubsection{Test Subsubsection}
\begin{theo}[label]
test
\end{theo}
\begin{theo}
test
\end{theo}
\begin{theo*}
test
\end{theo*}
\end{document}

numbers=enddot
class option.numbers=enddot
did a good job but still a few counters don't end with a dot e.g. theorem counters etc.