He has had Ant-Man, Giant-Man, Goliath and Yellowjacket.
The Ant-Man gear went to Scott Lang, and Pym abdicated that identity, and focused primarily on Giant-Man/Goliath. Then he sniffed some glue, went crazy and made Yellowjacket. In that guise he married Jan, and as a result later hit her. The Goliath name later went to Hawkeye as he used Pym Particles for awhile and gave up the bow. It kind of also went to Bill Foster who became Black Goliath. Giant-Man is just a stupid name and he didn't have any different abilities than he did as Goliath. For awhile he gave up being a super hero and chilled out with the West Coast Avengers as a tech guy, at this point he could make things grow or shrink at will, and he'd get in fights now and then, utilizing an arsenal of high tech weaponry that he kept shrunken in his pockets.
Most recently he went back to being Yellowjacket, wishing to use that name to atone for his past sins. For awhile there was another Yellowjacket, Rita DeMara, she was a part of the Master of Evil, saw it was a bad idea and became an Avengers ally. She died in the Crossing, leaving the identity open for Pym to snatch back up.
As of now, Pym is stable again, and he and Janet Van Dyne, the Wasp, are ready to get re-married, and they adventure as the Wasp and Yellowjacket.
Yeah. Hank Pym originally discovered the Pym Particles, but since then a few people have gone on to use them. Pym himself, Janet/Wasp, Black Goliath, Hawkeye, Atlas, Yellowjacket II, Scott Lang and Cassie Lang.