SA OC 135:11 reads:
There's someone who says that if the gabay called a kohen or levi and he's not there, he should not call another by name, because of the p'gam of the first one. Rather, he should go up [to the Tora] by himself.
The p'gam of the first one means, according to MB :40, "that they'll think that it became known meanwhile [i.e., after he was called] that he's pagum".
It sounds to me from this like the custom was to call people by name. That doesn't answer the question about a mandate, though.
However, I do know as a practical matter that S'faradi synagogues — or at least Syrian (and IIRC Moroccan) ones I've been in — do not call people by name, despite the apparent implication of the SA. (Ashk'nazi synagogues I've been in do, for the most part.)