NGS Style Manual‎ > ‎- G -‎ > ‎

Gulf

Capitalize when referring to the Gulf of Mexico:
  Gulf of Mexico, the Gulf
Gulf Coast (U.S. region)
Gulf Coast states
Gulf current

the Gulf region (U.S.)
Gulf Stream
Gulf waters
Other gulfs are always lowercase except in a place-name:
  the Persian Gulf
the gulf
Persian Gulf states

the gulf coast
Gulf of Corinth
Gulf states (for Arab states of the gulf)
Note that although the historical and internationally accepted designation is Persian Gulf,
many Arab countries use Arabian Gulf.

Where scale permits, National Geographic maps  include a note about Arabian Gulf.

If Arabian Gulf is used in text, it should be explained.