A few examples of loggers and levels that include the Stored Process name (and path):
2018-09-29T11:14:56,730 INFO [00000742] (App.SASSTP.RQ.LOG) 8:sasdemo - _PROGRAM=/Products/SAS Intelligence Platform/Samples/Sample: Hello World
2018-09-29T11:24:57,263 DEBUG [00000030] (App.SASXSTP) :sassrv - [00000004] STPXMVA Input arg: '_program' = /Products/SAS Intelligence Platform/Samples/Sample: Hello World
2018-09-29T11:24:57,275 INFO [00000008] (App.Program) 12:sasdemo - _PROGRAM=/Products/SAS Intelligence Platform/Samples/Sample: Hello World
... you may also want to add some log filter config to limit the output to what you want.
I assume that you are wanting this from outside the stored process itself e.g. audit logging? If the stored process wants to know what its own name/path is it can just use &_PROGRAM macro variable.