What Trump says and what he actually does are two different things.
Much of what he said he would do during his first presidency wasn't accomplished.
All anyone can do at this moment is speculate as to what he will do once he's inaugurated.
Obama renamed Mt. McKinley to Mt. Denali in 2015 and with that action signed by executive order through the secretary of the interior,
He could do that because that mountain is within Alaska's boundaries and it was something the state of Alaska wanted.
The US can rename it what ever they want, and the rest of the world can call it what ever they want.
This is not the same as the Mt McKinley situation. Trump cannot unilaterally change the name because it also borders Mexico and is an International body of water. Other nations are not obligated to recognise a name change and don't have to go along with it.
The United States and Mexico are both members of The International Hydrographic Organization, an organization which works to ensure all the world's seas, oceans and navigable waters are surveyed and charted uniformly, and also names some of them.