This has been a long time coming. Probably best to turn them into character tags. As far as the fandom is concerned, Project DIVA modules function more-or-less like individual characters. I felt a bit of hesitancy since there are situations where a different character wears another's module but those are far and few in-between and can just be considered cosplay.
Glancing through the current List of Project DIVA modules, the current names feel fine as is. Most of the modules are originally Western names/words in the first place.
The main problem I see are modules with extremely generic names (i.e "Angel", "Cute", "Dancer", etc) being very ambiguous and also possibly conflicting with possible future tag names. In such cases, I suggest appending "module" to them. e.g. Hatsune Miku (Angel module). For consistency's sake, it might even be better to do so for all modules.
P.S. That's gonna be a crapton of implications!