From the surface (37ft altitude) to 334.40 miles, the name is The Gulf. At 334.4 miles up, BOTH names are visible. From 334.4 to 1340 miles altitude, the name is Persian Gulf. Above that, the name layer for that area of water is not visible. At no time in the zoom from 39,205.98 miles out to the surface did it change names to anything other than the two shown - The Gulf and Persian Gulf.

I do, however, see one blatant error - The Gulf of Bahrain is misspelled.