You can do this by obtaining the caller tree by dbstack and parse the corresponding line of the calling M-file.
But I strongly recommend not to do this. The processing should not be based on the names of variables, because varaibales belong to the program, while the program should operate on the data. So mixing the program's source code with the operations on the data is a anti-pattern for clean programming. Such meta-programming increases the complexity of code dramatically. It is the opposite of the information-hiding principle in the object oriented programming. So even inputname is a strange command from this point of view.
Remember that such methods must fail, when the code is compiled.
When the names of the variables really matter, it would be a clean way to program this explicitly:
Data.A = 1:5;
Data.ReturnVariable = 'B';
Data = myfun(Data);
function Data = myfun(Data);
Data.(Data.ReturnVariable) = Data.A;
This is a little bit longer, but it is clean and clear. You cannot get obstacles like anonymous variables, as calls like this would cause with outputname:
field = 'asd';
S.(field) = myfun(A);