The name Morrissey is a boy's name meaning "descendant of Muiris". Morrissey and is often added to lists like Surname Baby Names and discussed in our forums with posts like "Choose Their Stage Names".
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).