Question about title.

Yes it IS Godzilla Raids Again, Not Godzillas Revenge, that came out 13 years later.

Why do you guys fight like this???
Fight Like this!!!

Well, you're incorrect on several points.

First, Godzilla, King of the Monsters -- the Americanized version of the actual original film, Gojira -- was released jointly in the US in 1956 by Trans World Pictures (credited on screen) and Joseph E. Levine's Embassy Pictures, to which the owners of Trans World had sold half the rights, and which handled its marketing and distribution. AIP never had anything to do with GKOTM, held no rights to it and had no financial or other interest in it, ever.

Second, the name "Godzilla" was not copyrighted by any American company -- it's a Japanese invention, the "international" name for Gojira, owned by Toho. In 1957, a company called AB-PT purchased the US rights to the original Japanese feature, Gojira no gyakushu, from Toho, planning to insert American scenes and heavily redo the script, similar to what was done to the original Gojira. Subsequently, AB-PT collapsed and its assets were acquired by Warner Bros. The producer of the American version, Paul Schreibman, revamped it into merely a dubbed version of the original (with narration and some padded footage added). It was his decision, not the studio's, to rename the monster "Gigantis" -- not for copyright reasons, as WB owned the rights to release the film in the US using the name "Godzilla", but because Schreibman got it into his head that the movie would do better using a "new" monster name instead of Godzilla. Since there had at that point been only one other Godzilla movie (the original), and the monster wasn't yet the household name he would become in the 60s, there was a particle of reason to this basically absurd, or pointless, decision. Several years later, after Godzilla had become hugely famous (and profitable) in a succession of movies, Schreibman admitted that renaming the monster had been one of the stupidest things he had done professionally, and that he should have kept "Godzilla". There was no legal impediment to his doing so -- it was simply a dumb decision driven by misguided box-office concerns.

This is why the dubbed version of the film was eventually retitled Godzilla Raids Again, under which name, as you say, it played for years, well into the 1980s. The idiotic thing about this was that, though they inserted a new (and clumsy) title card in the American version reading "Godzilla Raids Again", they didn't change the dubbing, so throughout the film the monster was still called "Gigantis"! Only since the 90s has the original film surfaced in the US, but the retitled name Godzilla Raids Again stuck, even to the original version, in spite of the fact that the actual translation of the Japanese film is "Godzilla's Counterattack".