Confer with your band. If you are not sure where to go with your band name, it's a good idea to sit down with the rest of your band. It's important your band members agree on your choice in band name to avoid causing unnecessary rifts, and you should encourage them to bounce ideas back and forth and build on your suggestions.
Identify any key phrases that you would like to include in your band name. If there is anything that is synonymous with your style of music or your band in general, you should try to incorporate it to help build your name. For example, if your lyricist is interested in the macabre, you may want something incorporating the word "death" or "tomb."
Use genre-specific band names. The rules that link band names to sub-genres of metal are by no means set in stone, but they can be used to come up with an appropriate name. To give some real-world examples, Metallica is a band that plays standard, straight-up metal. The name reflects that; it is simple and based around the key word "metal." Cannibal Corpse is a death metal band, and their name is much more brutal, evoking horrific images of reanimated corpses eating people. Look at other bands in your sub-genre (or intended sub-genre) and use similar ideas.
Think of a formula for a band name and invent variations based on it. For example, you could come up with a death metal band name easily by thinking of ways to dismember a body part or organ. Using this theme, you can come up with names like Brutalized Entrails and Lacerated Esophagus easily. Take an idea and have fun with it, and write down any good ideas you have. The English language is fantastically vast, and there are scores of good words to play with to come up with your name.
Use band name generators and websites as a last resort. Although generators can occasionally present good ideas, they could possibly be stumbled across by many other bands, and their inherent randomness means that they are devoid of individuality. Perhaps take a good suggestion such as Infected Funeral and add a personal spin.