The task can be done with a batch file with following command lines:
@echo off
setlocal EnableExtensions DisableDelayedExpansion
for /F "delims=" %%I in ('dir "%~dp0*-min.*" /A-D /B /S 2^>nul') do (
set "FullFileName=%%I"
set "FileNameOnly=%%~nI"
set "FileExtension=%%~xI"
setlocal EnableDelayedExpansion
if /I "!FileNameOnly:~-4!" == "-min" ren "!FullFileName!" "!FileNameOnly:~0,-4!!FileExtension!"
endlocal
)
endlocal
The command DIR executed by a separate command process started by FOR in background with %ComSpec% /c and the command line between ' appended as additional arguments outputs also file names like Test-File!-min.x.pdf with full path. For that reason the IF condition makes sure to rename only files of which file name really ends case-insensitive with the string -min like Test-File!-MIN.pdf.
Read the Microsoft documentation about Using command redirection operators for an explanation of 2>nul. The redirection operator > must be escaped with caret character ^ on FOR command line to be interpreted as literal character when Windows command interpreter processes this command line before executing command FOR which executes the embedded dir command line in a separate command process started in background.
For understanding the used commands and how they work, open a command prompt window, execute there the following commands, and read entirely all help pages displayed for each command very carefully.
call /? ... explains %~dp0 ... drive and path of argument 0 which is full path of the batch file which always ends with a backslash and for that reason concatenated with the wildcard pattern *-min.* without an additional backslash. %~dp0 can be removed to run DIR on current directory and all its subdirectories instead of batch file directory and all its subdirectories.
dir /?
echo /?
endlocal /?
if /?
ren /?
set /?
setlocal /?
See also this answer for more details about the commands SETLOCAL and ENDLOCAL.