Adam West was supposedly the mayor of Quahog RI and plays a comic exaggerated version of himself.
In Brockmire, a few different sportscasters play shittier version of themselves, most prominently Joe Buck who plays himself as a narcissistic elitist as Brockmire’s foil.
Point taken, I mis-read the OP.
Adam West in Big Bang Theory
I agree with some of your other examples, but not this one. The Lucy character in I Love Lucy is portrayed as a ditzy housewife with no practical sense, always getting herself into trouble of her own making. She cannot hold down a job when the husbands and wives decide to switch places, and is a complete failure when she and Ethel decide to buy a dress shop. The Ricky character is perhaps a more realistic portrayal of a less accomplished Desi Arnaz, but not Lucy.
Lucille Ball in reality was a strong-willed, intelligent actress who understood the television marketplace better than CBS executives did. She and Arnaz pushed the conservative old-timey sponsors into accepting new ideas that the sponsors strenuously opposed. Lucy prevailed, and helped make the show the incredible success that it was.
I disagree with this too, because she wasn’t playing a fictionalized version of herself, so she doesn’t count for the purpose of this thread. Her name on the show was Lucy Ricardo, née McGillicuddy, not Lucille Ball. She was a 50s housewife, not an actor / showgirl (though she wanted to be, the source of many zany shenanigans).
Likewise with many other TV shows created as a showcase for various actors / comedians and at least partially named after them. In ‘The Bob Newhart Show’ he played Bob Hartley - psychologist, not Bob Newhart - comedian. Likewise with his other shows with his name - different last name, different profession. Likewise with Rosanne Barr playing Rosanne Conner, née Harris, though her character on the show may have somewhat paralleled her life before she became a comedian.
About the only ‘show named after its main character’ example that I can think of off the top of my head that would count would be ‘Seinfeld’, in which Jerry Seinfeld - comedian, played a fictionalized, (possibly?) worse version of Jerry Seinfeld - comedian.
It looks like Bruce Campbell has not been mentioned yet. See My Name Is Bruce. Not sure if I would consider it a “worse” version of himself, but he definitely play himself for laughs.
Last night’s (5x05) The Boys had five of them (spoiled for newness): Seth Rogen, Will Forte, Craig Robinson, Kumail Nanjiani, and Christopher Mintz-Plasse.
Zach Galifianakis, of course, on “Between Two Ferns.”
Already mentioned in this thread, but the movie ‘This is the End’ had an overlap of three of those guys also playing worse versions of themselves: Seth Rogen, Craig Robinson and Christopher Mintz-Plasse.