A quick skim of HoE's list looked to me that a lot of the clubs had generic names, or weren't clubs at all- concerts would be given in ballrooms, or community halls, or the like. Nightclubs were still developing at the time, and places like the Cotton Club are so famous because they were still pretty unique.
Part of this is due to Prohibition being in effect- most people wanting to imbibe wouldn't be going to a large club, but to someplace in a back alley with a big thug asking them for a password (note: don't use "Swordfish"). Such places could have a jazz band to get people to stick around, or they could just be watering holes for barflies. They won't have fancy or eye-grabbing names, though; they probably won't have signs at all, but will just be known by word-of-mouth, with unofficial names like "Louie's Joint". So, really, it depends on what sort of atmosphere you're looking to evoke- high class or seedy.
Out of curiosity, what sort of music do you have lined up?