Would it be copyright infringement to use a trademarked name in part of a domain name for a web site?

Would it be copyright infringement to use a trademarked name in part of a domain name for a web site? The name I am considering using is a made up name of a character. A similar example would be ‘Shrek’, the animated character in the movie of the same title. It would be used in conjunction with other non-trademarked words, an example being www.shrekforthewin.com. The service I would be providing is in no way related to the actual character, though I do not know if that would make a difference. Does it change things if I would be making some money through advertisements and endorsements on the site?