Ariel Bender
Siouxie
Richard Hell
Rat Scabies.
Buck Dharma
Lux Interior
Captain Beefheart
Zoot Horn Rollo
Rockette Morton
Drumbo
The Mascara Snake
Ed Marimba
Then there’s the lead singer of the great Mexican rock (etc.) band Café Tacuba, who changed his name for every album.
I prefer Ted Cactus, but to each his own. 
Richard Cheese
Jerry Only
Jimmy Pop
Teresa Nervosa (thanks, punch line loser!)
Muddy Waters
Howlin’ Wolf (OK, they’re blues guys, but these are great stage names)
Dr. John, the Night Tripper
Stevie Wonder
The Ox/Thunderfingers
If we’re getting into nicknames rather than full pseudonyms, allow me to offer Brenda, Keith’s put-down name for Mick.
Johnny Rotten
Alice Cooper
The Edge
Gene Simmons (Chaim Weitz)
Paul Stanley (Stanley Eisen)
Elton John (Reginald Dwight)
Nelson Wilbury (George Harrison)
Otis Wilbury (Jeff Lynne)
Lefty Wilbury (Roy Orbison)
Charlie T. Wilbury, Jr. (Tom Petty)
Lucky Wilbury (Bob Dylan)
Adam Ant (Stuart Leslie Goddard)
Billy Idol (William Michael Albert Broad)
Does anyone in Rock actually use their real name? 
Not R’n’r but Reggae:
Yellowman.
It could have been worse, he could have entered politics.
Biff Byford
Geddy Lee
King Diamond