Gulf of Mexico is what it has been called so it makes no sense to rename it. Names often dont make sense plus spain and later mexico used to control more territory along the Gulf coatline. Unless you want to piss of one of our most important allies for no reason
I agree, the coastline is mostly shared between the two.
Since you brought up Turkey, they renamed themselves recently. Practically a lot of people just can't keep up every countries nuances and just use the old names. It's fine. It seems like a lot of people still use Bombay over Mumbai too ¯\_(ツ)_/¯
A funny thing: I’ve spent a considerable amount of time in Mumbai, and there definitely seems to be a significant number of native residents who still call it Bombay. It was to the point where we briefly wondered if this was referring to two different parts of the same city (south of the Sea Link bridge is Bombay, the rest is Mumbai, maybe).
Names are complicated! Germany/Deutschland, Holland/The Netherlands etc.
Indian government tried giving things 'post-colonial' names but not all of them stuck equally. I do think Bengaluru is a slightly cooler name than Bangalore though!