I don't know of a commonly agreed-upon term for that, unfortunately. "Utility maximizer", "VNM-rational agent", and "homo economicus" are similar to what you're looking for, but none of these terms imply that the agent's utility function is necessarily dependent on the welfare of others.

Rational self-interest?

Then what would the term be for a VNM-rational, moral anti-realist who explicitly considers others' welfare only because they figure in his utility function, and doesn't intrinsically care about their own utility functions?

"Utilitarian" and all the other labels in normative ethics are labels for what ought to be in an agent's utility function. So I would call this person someone who rightly stopped caring about normative philosophy.

To use an Objectivist term, it's a person who's acting in his "properly understood self-interest".