He began using "The Hulk" ring-name long before he went to the WWF (and the AWA), specifically, Terry "The Hulk" Boulder. He appeared on a TV talk show, along with Lou Ferrigno (star of "The Incredible Hulk" TV show). The host made a comment that Hogan was actually larger than Ferrigno, so Hogan started using "The Hulk" as his ring-name.
Vince McMahon SENIOR gave him the last name "Hogan" when he wrestled for the elder McMahon in the very late 70's. Of course, with his physical size and enormous muscles, along with his charisma and mic skills, "Hulk Hogan" got over with the fans, so he continued using that ring-name for the next few years in Japan and the AWA.