This is the same distinction as Russellianism vs. Fregeanism, except applied specifically to proper names. I think in the Philpapers survey, this question replaced the Russellianism vs. Fregeanism one.

Fregean: The meaning of a proper name is a way of conceiving of its bearer. Different names for the same bearer may be associated with different ways of conceiving, and thus have different meanings. For instance, "Superman" and "Clark Kent" have different meanings.

Millian: The meaning of a proper name is its bearer. The meanings of "Superman" and "Clark Kent" are identical.

Other: both can be true depending on the situation. This can be only meaningfully interpreted as a question of psychology (what goes on in people's heads), there's no way in which one method of ascribing meaning to names is 'truer' than the other so asking to choose between the two looks like a confused question.