There are/have been at least 7 bands with name Absence (or containing mainly it):
1) Italian vegan straightedge band formed in 1994, played their last show in Ieper in 2002.
2) German Melodic Death Metal band formed in 1996 (active)
3) Finnish Melodic Death Metal band (from Säkylä) formed in 2000 (active)
4) Finnish Thrash Metal/Hardcore band (from Saarijärvi) formed in 2000 (on hold)
5) Brazilian Death Metal band formed in 2002 (active)
6) The Absence, Thrash Metal/Melodic Death Metal/Gothenburg band from USA formed in 2002 (active))
7) German hardcore electronic music producer Oliver Fohrmann (active).
Plus, apparently there have been more projects (that are no longer active) with this name.
There's also an american hc/ska band (from saginaw, michigan) (currently re-uniting!!)