There are reasonably large populations of people who call the body of water either the Persian Gulf or the Arabian Gulf. I do not see that there can be a dispute over this.
That’s true if the question is “which name do people use colloquially.” But per OSM’s own wiki language quoted earlier in this thread, the name tag isn’t meant to just tally regional usage, it’s meant to record what’s “most widely internationally recognised.” For most contested place names there’s no external body whose actual job is to adjudicate that. But for this feature type, sea and gulf names specifically, there is one: the International Hydrographic Organization (IHO).
Their standard, Special Publication S-23 (“Limits of Oceans and Seas”), is directly checkable here: https://iho.int/uploads/user/pubs/standards/s-23/S-23_Ed3_1953_EN.pdf. The 3rd edition (1953) is still the one in force, not because nobody’s gotten around to updating it, but because a 4th edition was drafted in 1986 and again in 2002, and both collapsed, partly over exactly this kind of contested naming (the Sea of Japan/East Sea dispute has caused the same gridlock in IHO revisions since). It’s a standard that’s specifically survived repeated attempts to overturn it.
The distinction also shows up cleanly in ordinary reference data: Marine Regions’ gazetteer entry for this feature ( Marine Regions · Persian Gulf (IHO Sea Area) run by the Flanders Marine Institute, a real marine-science body) lists three English names, each with a cited source. “Persian Gulf” and “Gulf of Iran” are both credited to that same 1953 IHO standard. “Arabian Gulf” is credited to GeoNames, a crowdsourced aggregator, not a naming authority.
So I don’t think this is actually an unresolvable popularity dispute the way Derry/Londonderry is. There’s a specific, existing, checkable standard for exactly this category of feature, and it says Persian Gulf / Gulf of Iran. alt_name and name:xx can carry everything else, including Arabic-language and regional usage, without the primary name tag needing to sit out a dispute the relevant standards body has already settled.