He actually wrote Manic Monday under the pseudonym "Christopher". It was Sheena Easton's "Sugar Walls" where Prince used the Alexander Nevermind pseudonym.
Wikipedia says "Christopher," other internet sources say he wrote both "Sugar Walls" and "Manic Monday" as "Alexander Nevermind."
I don't have that CD by The Bangles, so I can't check the liner notes to be sure. Whichever pseudonym Prince used, it was still Prince who wrote the song. And I've now wasted more time on who wrote a mid-80s pop song than I should have today!
Thanks for reading the site,