They may not be canon, but reconstructions of the Promenade e.g. in Star Trek Online have only Quark’s.

Also, I found this picture of a Promenade directory on Memory Alpha:

It lists “Spacely Sprockets,” among other things, but no other bars.

Also, now I’ve got to go re-watch DS9:“Rivals” because I didn’t remember it at all, so thanks for that!