A few years back, a band named Green Jello changed its name to Green Jelly to avoid a dispute with the owners of the "Jell-O" trademark. While the group ultimately got terrific publicity from all the flack, having a name that steps on someone else's toes can be a serious problem. The most common difficulties don't come from naming your band after snack foods, vacuum cleaners, etc., but rather from another group that used the name before you did.
Your group name is protected by a service mark which is similar to a trademark--which is a name used for goods (like Heinz ketchup, Kleenex tissues, etc.) and a service mark is a name used for services (like airlines, dry cleaners, and musical groups). The rule is that you get rights in a mark by having it associated with you in the mind of the public. So if the fans think of you when they hear the group name, it's yours and no one else's.
In fact, you can even stop names that are different from yours but similar enough to confuse the public. For example, there's a famous case from the 1920s where Charlie Chaplin stopped someone from using the name "Charles Aplin" and there's even a more fun case where the Dallas Cowboy Cheerleaders stopped the porno film Debbie Does Dallas from calling its star an "X Dallas Cheerleader."
By the way, your association with the group name doesn't have to be nationwide--it can be only in your hometown. Let's take an example: Suppose you live in Tulsa, Oklahoma, and invent the name "Pukeheads." Using this name, you start playing locally in august, 1991 and build up a major buzz and fan base. Then, one day in 1994, you walk into the record store and find an album by a group from New York called "Pukeheads." What can you do?
Actually, you may be able to do quite a bit. If you were a Pukehead in Tulsa before the New York guys used the name in Tulsa (the date you started using it is key--you have to be first), you can stop them from distributing records in Tulsa. Even if they used the name first in New York, if you were first in Tulsa, that town is yours. They could, however, stop you from using the name in New York if they used it there first; and if they used it nationally before you, they might even stop you in Tulsa.
This gets pretty complicated and depends on the specific facts in each case. But let's assume that you own Tulsa. Since it's impossible for a record company to skip a specific market when it runs a national distribution system, if you own the name in Tulsa, you can effectively block them from using it on records in the U.S. This is a joyful result if you're in the band from Tulsa, but a nose-dive downer if you're a Pukehead from New York.
Note that your rights come from using the name, not from registering it. Registration means filing a public notice that tells the public you claim a particular name. When you use a name, the public begins to associate it with you. And if someone else uses the same name, the public could be fooled into thinking it's you, which is a no-no. So your most important rights are from usage, even though you do get some important rights from registering.
If you find a group using your name, or using a name that's similar to yours, you have to deal with it. Most of the time, you can contact the other group and work out a deal. If you find them and discover that they broke up or abandoned the name, they may have lost their rights and you don't even need to make a deal.
If they're still using the name, and if they're willing to change it, they'll want to get paid. The most common deal is the payment of a lump sum (usually in the range of $1500 to a few thousand dollars) in exchange for their drifting into the sunset. However, this is a tricky legal area and you'll need a knowledgeable lawyer to draw up the deal.
If you can't make a deal, then you have to change your name. Sometimes you can keep part of the name by adding something to it, but you need to add something distinctive that clearly separates you from the others. For example, if you were using the name "Silver" and found that it was taken, you might call yourself "Denver Silver." Again, this procedure is tricky, and you'll need legal help.