I've voted for OpenCATS (and I note that Russ has already registered opencats.org, which helps), simply because I think maintaining a link with the past is important, not least because it continues to recognise the immeasurably immense contribution of the original code by Cognizo.
That said, if the General Will (TM Jean-Jacques Rousseu) is that a new name should be chosen, I agree entirely with Asim that "speakability" is important, otherwise it is a disincentive to use. Although I'm sure no CATS code would ever be "running slowly today" - it is too lean for that!
So, to some suggested names, off the top of my head... I don't claim all (or indeed any) of them are any good, but they might at least spark somebody else off in the right direction...
ARTS - Applicant Recruitment and Tracking System, or just ART
DOGS - hopefully not a sign of relations with Cognizo, but nonetheless there for ausement, and Mac users will understand the idea of a dog as a visual metaphor for a search application... doesn't stand for much, although I used to use a CAD systems called Design Office Graphics System. But "The Dogs" has some connotations, certainly for the UK contingent. Domains might be tricky, but, just for info, dogsproject.com or thedogsproject.com is available. Come to think of it, thecatsproject.com is available, too...
Abaction - an old English word to describe "the stealing of whole herds of cattle, as contrasted with a few head" - quite apt for the headhunting game, at least. I used to have a headhunting business called Abaction, but it was a lot of years ago and I won't claim any rights
Felus - the genus name for the cat family. Helpfully, felus.net, for instance, is available.
ReCATS - Recruitment Candidate Application Tracking System or somesuch, also a play on the idea that the OS version could evolve into "CATS Reloaded" as it were. Again, recats.net is available, for instance.
Captcha - has some interesting connotations, and could be made to stand for something - CAts ProjecT something or other
If one stops worrying too much about domains (after all, Cognizo are offering this is ASP, this doesn't have to be as catchy a URL - thewhatsitproject.org is fine for now), then things can get a bit more free-form. So, in that vein...
ReNew - the new recruitment software (and other obvious connotations)
If one goes for the SAP approach to naming, I suppose just CPL could work - if anyone asks, it stands for Cats Protection League...
To take a reference from a film, RePet could be interesting, although the idea of cloning candidates isn't always appealing. But that could get you ReCATS (recats.org...)
Extending another idea, MARS - for Mainly Automated Recruitment System or somesuch - might work. Or even CARS (Cats-based Advanced Recruitment System or whatever).
I'd suggest Pears (pairs, putting candidates and clients together, etc... and a nod at Apple), but there's already a piece of recruitment software called Pears (well I think they've rebranded to IQX nowadays). In that vein, however, I suppose CUPPELS (as in couples) might work, and you could even have cuppels.com?
Right now there's a trend for "psuedo-element" names like Xenium and so on, particularly in IT or cosmetics & healthcare. So how about CATIUM? Catium.org is free... Or HIREUM (hire 'em)? "Powered by Catium" or somesuch could work
If one views the SaaS CATS as the "big brother" to the OS project, Kitten or Kittens could be a possibility.
Anyhow, enough brain-dumping for one session. Perhaps this will stimulate some further thoughts from others?