From the "Basic Info" tab in your profile settings, you can edit the name of your band. If only a few members have left and you decided to change the band name, simply put the new name of the band into the "Musician Name" field and add "Formerly Known As ___."
If your band has dissolved completely, use the "Musician Name" field to tell your fans so. Then post links and photos of your new project on your profile for your current fans to connect.
It's important to know that you cannot change your MySpace URL. You can find what your current MySpace domain is by clicking the "Listing Info" tab under "Edit Profile." There, you can change your genre of music; however, your URL is permanent. If you really would like a new MySpace domain, start a new page and announce your new band on your old page, as long as you're the one that retained access to it. If you do not have access to the old page, visit the homepage of the former site and view "all friends." There, you can go through each person and request him as a friend.