If you have "if called by X do this" I'd look for a parameter to express real knowledge about what's going on, like "if tuesday do this" or "if taxExempt do that". Checking the caller name tells me nothing of the real reason for the logic. Write code that tells a reader a story about what you're trying to do in the plainest way you can.
Also, a class that has to know who called it cannot be reused without change. If I want to call it from a new caller I have to open it up and add a
test for the new caller.
25 years ago I had a temporary assignment on a COBOL system where modules had dependencies on who called them. It was a nightmare to figure out or change and still makes me jumpy when this topic comes up.