[danaris]

...Was he?

Is "gets to rename any geographical feature in the general vicinity of the country on a whim" a usual power of the US President? I genuinely don't know the legalities around this, but given that, I would bet that most people who voted for Trump also didn't think they were giving him that power. (Whether they would have chosen to do so is a separate question.)

[glimshe]

Do electors of any politician ever understand the full extent of their candidate's powers? They vote on people under the assumption that the person is the best choice (not necessarily a "good" choice) for the job given the system already in place.

Answering your question: yes, the executive branch can change geographical names in the US. Obama did that too with Mt Mckinley. This power extends solely to the names as accepted by the United States. If Mexico wants to change the gulf's name to "Gulf of the Aztecs" or "Gulf of qetwyetwdhxysysheussg", it can do that too.

SHOULD they do it? Now that's a different question.