Substring of filename in LaTeX

% File name: DoctorStrange.tex
\documentclass{article}
\usepackage{xstring}
\begin{document}
    \StrBehind*{\jobname}{Doctor}% <---- Note the starred variant
\end{document}

gives

Certain TeX commands like \jobname (as is in your case) expand into strings made of characters with catcodes 12 and 10, whereas ordinary letters from the alphabet is given catcode 11.

The xstring package commands, as noted in the package documentation (Section 3.4, under Catcode and Starred Macros), take catcodes into account during comparisons, and so Doctor is not found in the \jobname because they have different catcodes.

To solve this, xstring package provides a starred variant of its commands, in this case \StrBehind*{<strA>}{<strB>}, which detokenizes the two string arguments, and as the documentation puts it:

...everything is converted into chars with "harmless" catcodes.

which will then yield the desired result, as above.

The characters in \jobname are “stringified”, which roughly means that your input Doctor (where the characters are letters) is not the same as the Doctor in \jobname (where they are nonletters).

You can use the “agnostic” version of \StrBehind or a similar category code agnostic function of expl3:

\documentclass{article}
\usepackage{xparse}

\ExplSyntaxOn
\NewDocumentCommand{\nodoctor}{o}
 {
  \tl_set:NV \l_tmpa_tl \c_sys_jobname_str
  \regex_replace_once:nnN { \A Doctor } { } \l_tmpa_tl
  \IfNoValueTF { #1 }
   {
    \tl_use:N \l_tmpa_tl
   }
   {
    \tl_new:N #1
    \tl_set_eq:NN #1 \l_tmpa_tl
   }
 }
\ExplSyntaxOff

\begin{document}

\nodoctor

\nodoctor[\thisname]

\texttt{\meaning\thisname}

\end{document}

In the optional argument you can specify the name of a macro that will contain the name. If you prefer that the text is treated as letters, for subsequent comparisons, you can use \tl_set_rescan:Nnn (actually a variant thereof):

\documentclass{article}
\usepackage{xparse}

\ExplSyntaxOn
\NewDocumentCommand{\nodoctor}{o}
 {
  \tl_set:NV \l_tmpa_tl \c_sys_jobname_str
  \regex_replace_once:nnN { \A Doctor } { } \l_tmpa_tl
  \IfNoValueTF { #1 }
   {
    \tl_use:N \l_tmpa_tl
   }
   {
    \tl_new:N #1
    \tl_set_rescan:NnV #1 { } \l_tmpa_tl
   }
 }
\cs_generate_variant:Nn \tl_set_rescan:Nnn { NnV }
\ExplSyntaxOff

\begin{document}

\nodoctor

\nodoctor[\thisname]

\texttt{\meaning\thisname}

\newcommand*{\checkthisname}{Strange}

\ifx\thisname\checkthisname SUCCESS\else FAILURE\fi

\end{document}