There are at least 15 bands by this name.
1) Abyss was a hardcore band from Germany, active in the early to mid 1990's. They shared the stage with bands like acme, systral, age, etc. They released a Self-Titled 7" and a split double 7" with the American hardcore band Iconoclast.
2) Mid 90's Black Metal project of the members of Swedish death metal outfit Hypocrisy.
They released two albums: "The Other Side" (1994) and "Summon The Beast" (1996). The correct tag is the abyss. Read more on Last.fm