I am using fake names for this question.
Jane Jones is the daughter of Julie ___ and Bob Smithers. Julie and Bob were not married. They lied, and Jane’s birth certificate says “Smith.” Jane later became known by her stepfather’s name, Jones.
With a source actually saying “Smith,” I wouldn’t want to ignore it, but would you put it in GEDCOM as a NAME (and if so, what TYPE), or would you put it as a NOTE on the BIRT or on the NAME /Smithers/? (Actually, I'd not put "Smithers" on her but it would certainly be on the biological father.)
I'm not aware of any living people with this issue, but my own grandmother did often get called by her step-father's name even though she was not officially adopted.