Look at band lists or band name generators for an idea on your own name. Make a list of the different names you enjoy. Pick out the ones that stand out and are creative and catchy. Determine which of these bands have seen the most success in your preferred genre and make a note of the names. Figure out which ones work and which ones are just not good.
Consider a short name. Keep the name at two or three words; these kinds are easier to remember. Make the name an emotion or a vivid image, or try to make it something with a story and meaning behind it. This will help it remain in vogue years later.
Stick to the genre. Avoid naming your band something along the lines of "Servants of Jesus" unless you are either a Christian band or an ironic metal band. Of course, it isn't mandatory to keep in your genre. For example, a rock band does not have to be called "Stone Warriors" or "Kings of Rock," but it would be best not to name it "Blue Cowboys" lest the name confuse its new listeners.
Ensure your name is one-of-a-kind. Check with websites such as GarageBand to confirm whether or not another band has that name. Use a unique name to avoid lawsuits, confusion and angry fans. For example, naming your band "The Beatles" will probably not work.