The Pocket novels of recent years have established fuller naming conventions for Andorians, and Tellarites (in fact, I happen to be the one who came up with the Tellarite naming pattern now used in the books, or at least the prototype for it). The '80s novels established fuller names for Klingons (in John M. Ford's The Final Reflection
and Romulans (in Diane Duane's Rihannsu novels), but those naming patterns aren't generally used in tie-ins anymore. But you still do see Romulans in the novels with two names. The current Praetor in the novel continuity is Gell Kamemor, and the books have given the Romulan Commander from "The Enterprise Incident" the name Liviana Charvanek.
Canon has established that a Klingon's full name includes a patronymic/house designator, such as "Worf, Son of Mogh." (Although since he was adopted, his full legal name should be Worf Rozhenko.) I sometimes wonder if "Sarek, child of Skon, child of Solkar" is a translation of the full Vulcan family name.