Columbo/WMG

Lt. Columbo deliberately obscures his first name as protection from Death Notes
This ties in with the Death Note theory that Columbo is L's grandfather. The family has known about the Notes for some time, and Columbo hides his first name from everyone in case one comes up.
 * Columbo also suggested L's name after the initialism of their esteemed ancestor Linnaeus.

Lt. Columbo is the mentor to Robert Goren
At some point, Goren studied Columbo's full case history and his methodology, learning as much as he could from them and then adapting them to his own use.

Lt. Columbo is a sociopath.
He lies without hesitation in order to catch the culprit. He even fakes feelings. He once faked being in love.

His greatest thrill is using the legal system to kill his victims. Yes, some of his victims do get killed -- the death penalty was legal in California during most of the original run.
 * Would this make Columbo a proto-Dexter?

Like many sociopathic killers, he sees himself as smart. He's very meticulous despite appearances. He gets an extra thrill out of catching the most cunning killers with the most unusual evidence.

He does not carry the real evidence around with him
Come on, this is not a stupid man. It's rather likely that Columbo obtains copies of the evidence to haul around with him. While he has displayed the actual evidence on occasion he's probably not going to put murder bullets in his pocket or into paper bags where they could be lost or tainted. If he really was doing this, almost all of his cases would be thrown out.

Columbo and Quincy are set in the same universe
Gary Walberg, the actor who played Lt. Monahan in Quincy showed up as an unnamed police sergeant in an early Columbo film Lady In Waiting. Maybe he later got promoted and moved to another precinct?