Batch (.bat): get the name of the first script, not the current one

This batch detects the name of the caller script or even if it's called directly from the command line

@echo off
setlocal DisableDelayedExpansion
set "func=%~0"
for /F "delims=\" %%X in ("%func:*\=%") do set "func=%%X"
if ":" == "%func:~0,1%" (
    goto %func%
)
REM *** Get the name of the caller
(
    (goto) 2>nul
    setlocal DisableDelayedExpansion
    call set "caller=%%~f0"
    call set _caller=%%caller:*%%~f0=%%
    if defined _caller (
        set "callType=batch"
        call "%~d0\:mainFunc\..%~pnx0" %*
    ) ELSE (
        set "callType=cmd-line"
        cmd /c "call "%~d0\:mainFunc\..%~pnx0" %*"
    )
    endlocal
)
echo NEVER REACHED
exit /b

:mainFunc
echo :mainFunc of %~nx0 arg1=%1 is called from '%caller%'/%callType%
exit /b

It uses the fact, that a (goto) statement will remove one level from the stack.
This results into leaving the current batch file and %~f0 will be the name of the caller script (and %~0 the current function of that batch) or the text %~f0 in the case of called from the command line.

Then the own script is called again with "%~d0\:mainFunc\..%~pnx0"

External Script

For easy use you could add a helper batch file.
Use it in your own scripts with this line

@echo off
<:GetCaller <nul call GetCaller.bat myCallerVar
echo This batch was called from "%myCallerVar%"

Name the helper batch file GetCaller.bat

@echo off
setlocal DisableDelayedExpansion
set "func=%~0"
for /F "delims=\" %%X in ("%func:*\=%") do set "func=%%X"
if ":" == "%func:~0,1%" (
    goto %func%
)

REM *** STEP1
REM *** Get the filename of the caller of this script, needed for later restart that
(
    (goto) 2>nul
    setlocal DisableDelayedExpansion %= it could be reenabled by the GOTO =%
    set "_returnVar=%~1"
    call set "_lastCaller=%%~f0"
    call set "_argToLastCaller=%%*"
    call "%~d0\:Step2\..%~pnx0" %*
)
exit /b %= This is never reached =%

:Step2
REM *** STEP2
REM *** Get the filename/cmd-line of the caller of the script
(
    (goto) 2>nul
    (goto) 2>nul
    setlocal DisableDelayedExpansion %= it could be reenabled by the GOTO =%    
    set "_returnVar=%_returnVar%"
    set "_lastCaller=%_lastCaller%"
    set "_argToLastCaller=%_argToLastCaller%"
    call set "caller=%%~f0"
    call set _caller=%%caller:*%%~f0=%%
    if defined _caller (
        set "callType=batch"
        call "%~d0\:Step3batch\..%~pnx0"
    ) ELSE (
        set "callType=cmd-line"
        cmd /c "call "%~d0\:Step3batch\..%~pnx0" "
    )
    endlocal
)
exit /b %= This is never reached =%

:Step3batch
REM *** STEP3 Restart the requester batch, but jump to the label :GetCaller
call :GetCaller
exit /b %= This is never reached =%

:GetCaller
REM *** This uses the trick, that starting a batch without CALL will jump to the last used label
if "%_returnVar%" NEQ "" set "%_returnVar%=%_caller%"
%_lastCaller% %_argToLastCaller%

echo #6 never reached

I think the easiest way of doing this would be to pass the filename of the first batch as a parameter to the second, like this.

REM First.bat
call Second.bat %~n0

REM Second.bat
echo %1

Hope this helps!

Store the value of %~n0 in a environment variable before calling second.bat