There is more than one band with this name: a British NWOBHM band, a Serbian Black Metal band, a French Grind/Black Metal band, a Japanese Visual Rock band. 1) Satan (UK) was an nwobhm band formed in 1979.
Satan would change their name to Blind Fury after the release of their debut Court in the Act in 1983. The former singer Brian Ross was replaced by Lou Taylor who was in Satan once before and himself was also, ironically, replaced by Brian Ross.
After they released Out of Reach in 1985, they changed their name back to Satan and Michael Jackson (not the pop star) joined on vocals.