The OSM Community discusses the Trump Administration's renaming of "The Gulf of Mexico" to "The Gulf of America"
(community.openstreetmap.org)
Check the community discussion thread (linked in the OP). I'm not sure they cover the Persian/Arabian Gulf specifically, but in general terms your question is likely answered in that thread.
TL;DR: There are various tags, prefixes, suffixes, whole nine yards for documenting all the different types of names.