The name Morrissey is a boy's name meaning "descendant of Muiris". Morrissey and is often added to lists like Musician Baby Names and discussed in our forums with posts like "Makeover name game: from one gender to the other".
From the experts:
When British rocker Steven Patrick Morrissey decided to use his last name alone, it became a viable option for baby namers, a lot cooler than Morris or Maurice, with the nice three-syllable lilt of of such other Irish surnames as Finnegan and Flanagan. It can also be spelled Morrisey.
Morrison is a related possibility, also with musical ties, to Irish singer-songwriter Van (born George Ivan).