What makes a cool band name really depends on the music genre of the band and the target audience. Possible names could be: "Strip Of The Idiot," "Somewhat Reindeer," "Underneath Premise," "Whizz Heretic," or "Supermarket Weasel," among others.
One way to come up with the right name for a band is to make it personal. To do this, the band first makes a list of relevant words. Second, they should brainstorm on those words and come up with all the possible other words that are somehow connected. Later, by combining the words in the list, the band members can make a second list with all the suitable band names. Finally, they should check if some of the names are being used by other bands before making their final choice. Some free tools are available on the internet that can generate band names automatically. One such example can be found at BandNameMaker.com. Most of these tools also allow the users to include a word of their choice.