They always always been consistent on who falls in which camp, but my assumption is as follows:
(P..S. I'm not bothering with listing "aliens of the week")
-Son'a / Ba'ku
-Bajorans (family name, then given name)
-Trill (In joined Trill, symbiont's name replaces host's family name)
Now this is just my opinion and there are exceptions (M'Kota R'Cho for the Klingons. Alidar Jarok and Telek R'Mor, among others, for Romulans. Par Lenor for Ferengi. Spock's supposed "unrponouncable" last name for Vulcans) But the majority of individuals from a species point to one, I'm inclined to believe that one.
I'd also point out that some, like Thy'lek Shran, are from split second data screens that are sometimes dubious. I'd further point out that some may not be a first and last name, but simply one name with two words (like the surname "Van Gogh").
A few races I'm on the fence about
: Some of the Xindi may have one or the other, for instance. We've only had one named Tholian and Gorn in canon, so that's not enough to rule one way or the other, IMHO. The Kazon, I think are kind of vague, with the earning of names and all.
What do you think?