The first wise guy who says “Lieutenant” gets a slap. Anybody who says “Christoforo” gets two slaps, one for being a wise guy and one for trying to show off his or her erudition. 
Never officially revealed. DVD technology allows freeze-framing that seems to show his first name as “Frank” on one occasion where he showed his badge, but it’s debatable whether the creators intended this, or if it was just a throwaway prop that no one was supposed to be able to read.
Officially, he never had a first name.
However, in one of the first Columbo movies, there’s a scene in which he displays his badge. His handwritten name indicates “Frank Columbo.” However, it was never, ever, ever used in a “Columbo” movie.
There’s some info on the subject here.
BTW, I think that scene was a “lost” scene. That is, it was a syndication cut, and was not seen in over 20 years.
How many slaps for “Kate”?
Does Mrs Columbo actually exist, or is she just an interrogative device that the Columbo character invented?
There is some evidence that she actually existed.
I have a trivia encyclopedia which gives Philip as Colombo’s first name, this work entitled The Complete Unabridged Super Trivia Encyclopedia (Brooke House Publishing, LA, 1979) by a Mr. Fred L. Worth.
Mr. Worth gives this entry an asterisk with the comment ‘One of the best kept trivia secrets’. However, I have been advised of the author’s dubious record in veracity on more than one occasion.
Mr. Worth intentionally made up the “Philip” first name in order to catch thieves who stole information from his book. Worth used the “Philip Columbo” trap in an unsuccessful lawsuit against Selchow and Righter over the Trivial Pursuit board game, in which at least 1/4 of the questions (including “What’s Columbo’s first name?”) came from Worth’s book. “Frank” is the closest thing to a correct answer. More information can be found in Ken Jennings’s (yes, the Jeopardy! guy) book Brainac: Adventures in the Curious, Competitive, Compulsive World of Trivia Buffs.
Well, in the episode “Troubled Waters,” which took place on a cruise ship that the Lieutenant was vacationing on, at least one character (a crewmember) said he saw the Mrs., so unless the Lieutenant has his personal Reality Distortion Field <tm>, I think it’s safe to say she exists, even ignoring “Mrs. Columbo.”
(In a more recent flick, when one of Columbo’s nephews gets married, he mentions his wife in front of this relative without being contradicted. Of course, this particular movie was quite unusual for the series to begin with, so YMMV.)
I used to have the CUSTE in paperback form as a young squirt. I remember having the impression that no one who had gathered up such a diverse and far-flung assortment of minutiae could possibly have cared to check all, or indeed possibly any, of them. The guy was clearly driven by one overweening compulsion: to acquire and compile.
Although, as mentioned, the Columbo fact was Worth’s own creation, it is true that many of Worth’s facts are either apocryphal or outright false. According to Jennings’s aforementioned book, critics refer to him as “Fred Worthless” and indeed do not accept his books as resources for trivia contests. Worth is still alive and is working on his pet project, an in-depth book of information about Hollywood actors.