Plus, it's the opposite of weird. National reasons are the most frequent cause for renaming areas after hundreds of years.
Additionally, the order doesn't change the name of any gulf along Mexico's Eastern shoreline. So whether they're "up for it" is inconsequential.
'Gulf of the Americas' would make more sense in that case. But that doesn't project the intended message from the new administration.
You can justify it however you want, but the intention was not to be inclusive and I think that's pretty clear. Unless talking about annexing Greenland and absorbing Canada are also just ways of making us one big happy family, I think the intention of the name is clear, regardless of how much sense one can force it to make after the fact.