>But because Trump did it, some Americans find this inherently problematic,
It's not "because Trump did it".
It's very unusual for geographic place names to be renamed at the whim of a single politician. It's extremely unusual for it to happen by fiat, so quickly. It's absolutely unheard of for a feature so large, and shared by more than one country, to be renamed in this way in the modern era.
Wasn’t it Obama who renamed Mt. McKinley by fiat after 100 years, also for political reasons? This is no more important than that decision. Both Presidents had the authority. And while the Gulf itself is shared, there’s no reason both countries automatically call it the same thing. After all, the name actually used by Mexico is in Spanish anyway.
> The name of the highest mountain in North America became a subject of dispute in 1975, when the Alaska Legislature asked the U.S. federal government to officially change its name from "Mount McKinley" to "Denali".
Besides already being the original indigenous name for the mountain, "Denali" was also the name already in use by many locals and outdoor enthusiasts elsewhere. It was already the name officially used by the Alaska state government, and the state had formally requested the federal government do that same way back in the 70s. Accepting that request is far from changing the name "by fiat" – especially not to a newly invented name that no one was using or asking for.
And that's before you even get into the difference between choosing a name out of respect for an original indigenous name vs. an intentionally jingoistic and self-aggrandizing name chosen to represent a new area of imperial possessiveness.
Considering the word "Mexico" comes from the indigenous people of the region while "America" was a name brought by European colonists... I'm not sure you can really say both of those share the same air of imperial possessiveness.
It's not "because Trump did it".
It's very unusual for geographic place names to be renamed at the whim of a single politician. It's extremely unusual for it to happen by fiat, so quickly. It's absolutely unheard of for a feature so large, and shared by more than one country, to be renamed in this way in the modern era.