Trivia: While Columbo's first name is never said, "The Trivia Encyclopedia" by Fred L. Worth listed his first name as "Philip." When the board game "Trivial Pursuit" used this fact as a question, Worth sued "Trivial Pursuit" for copyright infringement because he had actually made up that fact to catch anyone violating his copyright, the same way a mapmaker or dictionary company would add something fake to catch unauthorized copiers.
Trivia: Columbo's first name is never mentioned throughout the series. However in a few episodes, such as "Dead Weight", "A Matter of Honor" and "Death Hits the Jackpot" he flashes his badge and the name "Frank" can clearly be seen.
Trivia: Peter Falk's real-life wife appeared in 6 episodes, each time as a different character.
Trivia: Columbo's wardrobe for the show was Peter Falk's own clothes.
Answer: In the show, he was already a Lieutenant. A promotion would put him in the next rank up, which for the L.A.P.D. would be Captain. However, some of a Captain's duties would be overseeing other officers and ensuring they're compliant with policies, regulations, and standards. It would also most likely take him out of the field. This is something Columbo has no desire for as he rarely goes to police HQ's. Nor does he show interest in compliance and standards (for example, not going to his semi-annual evaluation at the firing range). However, he could still be assigned to a higher pay grade based on expertise, which is a form of promotion that does not include rank advancement. This would be going from Lieutenant I to Lieutenant II. I don't believe in the show it's ever started what his pay grade is. Although, in s02e01 (I believe) he mentions making $11K a year. Whether or not this was a true statement on his part, if you could find pay scale information for an LAPD Lieutenant in the 70's, it could give you an idea of his pay grade.
Bishop73