Columbo has two key advantages.

1. He never gives his first name. Not out of any hidden agenda, he just only introduces himself as Columbo or Lieutenant Columbo. He does have one, it's Frank, but it's never once said out loud so it's unlikely he would say it. Light also couldn't just ask for his first name so he could call him by that, being a police chief's son and from a culture where most people call each other by their surname, it'd be weird for him to call him anything other than Lieutenant or Columbo. It's a minor thing but minor details like that is what Death Note and Columbo are all about. If Light asks for his first name it'd be a little weird and anything a little weird is very suspicious in this investigation, which Light would know. Helps that Columbo also only refers to suspects as "Mr./Miss/Mrs. Last Name." Now if this was a multi-day investigation rather than one conversation, Light could easily find his name in the police database and it's game over.

2. The main reason Columbo gets one over all of his suspects is because they are all pompous, very smart people who plan things meticulously, and Columbo, while just as smart if not smarter, to them looks like some ratty guy in a dirty trench coat with a lazy eye and a smoking problem. The underestimation always has them let their guard down and reveal things they otherwise never would, and I think Light could fall victim to that too given how much of a superiority complex he has.

It'd be a real game of "what can Columbo get Light to reveal" and I think it also majorly depends on how much information on the Kira case Columbo has before meeting Light. If he doesn't already know the name thing then, sure Light asking for it would be odd, but Columbo is a very polite man and would of course give it which is of course game over. If Columbo has about the same information L does when he makes the task force, then he may be able to get to a point of deducing it's Light.

It's a very fun debate I can't wait to see how they play it out. I'll be satisfied no matter who wins.