Instead of redefining the environment mdframed I suggest the following.
The definition of a new key is very simple. So I recommend the definition of a new key e.g. digressiontitle This can be done by:
\mdf@do@stringoption{digressiontitle=={Digression}}
whereby the word Digression is the default value. You can change it.
The value of this option is saved in the macro \mdf@digressiontitle and can be used inside the definition of the style. This is done in the example.
In the next step I suggest the using of \newmdenv with a specific digressiontitle. (For more information about the command \newmdenv see the documentation.
So you can write:
\newmdenv[style=digressionarrows,digressiontitle=Info]{info}
\newmdenv[style=digressionarrows,digressiontitle=Side note]{sidenote}
And use:
\begin{info}
\lipsum[1]
\end{info}
\begin{sidenote}
\lipsum[1]
\end{sidenote}
which leads to the following output:

\documentclass{article}
\usepackage[framemethod=tikz]{mdframed}
\usetikzlibrary{calc,arrows}
\makeatletter
\mdf@do@stringoption{digressiontitle=={Digression}}
\tikzset{
excursus arrow/.style={%
line width=2pt,
draw=gray!40,
rounded corners=2ex,
},
excursus head/.style={
fill=white,
font=\bfseries\sffamily,
text=gray!80,
anchor=base west,
},
}
\mdfdefinestyle{digressionarrows}{%
singleextra={%
\path let \p1=(P), \p2=(O) in (\x2,\y1) coordinate (Q);
\path let \p1=(Q), \p2=(O) in (\x1,{(\y1-\y2)/2}) coordinate (M);
\path [excursus arrow, round cap-to]
($(O)+(5em,0ex)$) -| (M) |- %
($(Q)+(12em,0ex)$) .. controls +(0:16em) and +(185:6em) .. %
++(23em,2ex);
\node [excursus head] at ($(Q)+(2.5em,-0.75pt)$) {\mdf@digressiontitle};},
firstextra={%
\path let \p1=(P), \p2=(O) in (\x2,\y1) coordinate (Q);
\path [excursus arrow,-to] (O) |- %
($(Q)+(12em,0ex)$) .. controls +(0:16em) and +(185:6em) .. %
++(23em,2ex);
\node [excursus head] at ($(Q)+(2.5em,-2pt)$) {\mdf@digressiontitle};},
secondextra={%
\path let \p1=(P), \p2=(O) in (\x2,\y1) coordinate (Q);
\path [excursus arrow,round cap-]($(O)+(5em,0ex)$) -| (Q);},
middleextra={%
\path let \p1=(P), \p2=(O) in (\x2,\y1) coordinate (Q);
\path [excursus arrow](O) -- (Q);},
middlelinewidth=2.5em,middlelinecolor=white,
hidealllines=true,topline=true,
innertopmargin=0.5ex,
innerbottommargin=2.5ex,
innerrightmargin=2pt,
innerleftmargin=2ex,
skipabove=0.87\baselineskip,
skipbelow=0.62\baselineskip,
}
\makeatother
\newmdenv[style=digressionarrows,digressiontitle=Info]{info}
\newmdenv[style=digressionarrows,digressiontitle=Side note]{sidenote}
\usepackage{lipsum}
\begin{document}
\begin{info}
\lipsum[1]
\end{info}
\begin{sidenote}
\lipsum[1]
\end{sidenote}
\end{document}