I'll probably stop posting much about Stephen Colbert in a day or so but I wanted to direct you to a piece by Ian Crouch about Colbert's screen character and how Colbert has managed to disappear totally into the character but still manage to remind all but the dumbest people that it is, after all, just an act.
And it's really been quite a feat. I suspect in classes that teach improv comedy, Colbert's ability to ad-lib interviews in that character will long be pointed to as a very high watermark in the art of improvisation. I can't even think of what might come close.
But you wonder — well, I do at least — if he ever regretted tagging that character with his own name instead of drawing a line of separation as Bill Dana did with Jose Jiminez, Paul Reubens did with Pee-wee Herman, Jim Varney did with Ernest P. Worrell and Cliff Arquette did with Charley Weaver. Or if he regrets it now. If he'd named the character something else, it could become part of his repertoire, the way Martin Short could be Jiminy Glick for one part of a show and be himself for other portions. I also wonder if something he might do on his Late Show is actual sketches, the way Johnny would occasionally bring us The Mighty Carson Art Players.