"I thought doing it this way the variable "jobname" is automatically returned to the workspace after the function is done."
Nope, nowhere in the MATLAB documentation does it state that.
"How can I use the "jobname" variable?"
Have you tried calling the function with an output argument, just like the introductory tutorials show?:
myout = FEM_Rechnung(D_klein, R_mitte,job,index);
%^^^^^^^ you need to assign the output to a variable.
Note that the names of variables used inside a function are (and should be) unrelated to the names used outside the function. You might use the same name, but that is simply coincidence and of no importance to MATLAB.
