Can a band use a name that is already trademarked?
Rarely, a band may use a trademarked name. For example, a mark that is primarily a surname does not usually qualify for protection under federal trademark provisions, unless the surname becomes well-known or acquires a "secondary" meaning. Sometimes, a trademarked name can also be challenged and defeated if it is too broad. However, if a last name acquires a secondary meaning in the marketplace (e.g., Sears, McDonald’s), it cannot be used by others, regardless of its trademarked status. In order for a band to register a mark that has already gained secondary meaning, permission from the namesake must be obtained.
Similar Trademarked Names
There are also cases where even a name that is similar to the trademark cannot be used. "The Doors," for example, might be a great theme song for a company such as Home Depot, but because the original band continues to create royalty checks for its label and surviving band members, it cannot be used for that purpose without explicit permission. Nor could a singer whose last name is Dohr (pronounced like "door") create a band with that name, especially if their style of music was similar to "The Doors." This would likely be seen by courts as either deceptive, or likely to confuse/dilute the value of the original copyright material and trade name. There are some exceptions for political use or satire, such as skits in Saturday Night Live.
Contracts and Court Battles
As another example, Prince, in expressing his art through his choice of name and promotional materials, reacted to his record label’s claim to controlling his name by legally changing it to The Artist Formerly Known as Prince (TAFKAP). Prince's case shows that occasionally you can lose just some of the rights to your own surname. Similarly, some former band members may not be able to use a trademarked band’s name (e.g. - Band "XYZ") in promoting their act, but they are allowed to identify themselves as “a former band member in Band XYZ.”
Most rap artists today actually learned from the long-running TAFKAP case, and include in their agreements that they retain almost all rights to the commercial uses of their name, in all forms, from video to musicology. An increasingly complicated aspect of being a last name band has been web site ownership. Since 1999, the Big Five (BMG, EMI, Sony, Universal Music, Warner) have all used (or tried to use) standard contracts, giving their label control over commercial uses of artists' names and web sites.
There are also some cases in which a trademarked name is not commercially active. In these cases it's possible that the name has been abandoned and a new trademark can be issued (at least for use as a band name). For this, or any other questions about trademarked names, you should speak to a lawyer for help.