I think it goes out of style in the early 60's. I don't know if it's actually true, but I heard that during a briefing, R McNamara thought the F4H and F110 (both Phantom II's, but USN and USAF variants) were two totally different planes and was embarassed afterwards when he found out they weren't and so changed everyone to a common naming system. Those two became the F-4A/B and F-4C.
USN used:
F = Grumman (F4F Wildcat, F8F Bearcat)
U = Vought (F4U Corsair, F8U Crusader)
H = McDonnell (F4H Phantom, F3H Demon)
D = Douglas...etc...
1st letter indicated role (F fighter, A attack, etc), 2nd was the design in sequence for that company (3 would mean that company's 3rd design) and 3rd was the company designator. I kinda liked the system. :-)