On The Mary Tyler Moore Show, Ted Knight played Ted Baxter.
What other regular cast members on TV have shared first names with their characters?
On the Mary Tyler Moore show? 
I’ve read somewhere on the Internet (so it must be true) that Tony Danza wouldn’t respond to any other name except Tony, so his characters are always Tony. Looking at his IMDB entry, he did play characters with different first names, but he was Tony in Taxi, Who’s the Boss, the Tony Danza show, and Hudson Street.
Woody Harrelson played Woody Boyd on Cheers.
I remember reading somewhere that this was entirely a coincidence, as the character was written before Harrelson even auditioned, but I have nothing to back that up.
Tons.
Most sitcoms that are ‘vehicles’ for comedians do this.
Andy Griffith / Andy Taylor.
Lucille Ball / Lucy Ricardo.
Bob Newhart / Bob Hartley.
Jerry Seinfeld / Jerry Seinfeld.
Danny Thomas / Danny Williams.
Are you just yanking our chains, Bricker?
No, and it kind of floors me to realize that even in my example I completely skipped over Mary Tyler Moore as Mary Richards to focus on Ted Knight / Baxter. I guess I was subconsciously thinking of actors others than the ones with shows named after them, so Andy Griffith and Jerry Seinfeld would not count, but Tony Danza does.
Here’s an odd one. In the Shadow radio dramas, Margot Lane is the Shadow’s companion. She was named after Margot Stevenson. The first person to play her was Agnes Moorehead. The second was Margot Stevenson.
Emeril
The Bob Newhart Show and Bob
Not quite what you’re asking for, but the actors and roles in Robert Altman’s Images were:
Susannah York : Cathryn
Rene Auberjonois: Hugh
Marcel Bozzuffi: Rene
Hugh Millais: Marcel
Cathryn Harrison: Susannah
On The Games (an Australian comedy about the organizing of the Sydney Olympics[sup]*[/sup]) pretty much all the characters had the same names, full names even, as the actors who played them. John Clarke, Bryan Dawe, and Gina Riley played John Clarke, Bryan Dawe, and Gina Riley, respectively. The names of fictional characters don’t really have any significance, why not just use their real names? Sam Neill was in one episode, but I don’t know if the full name of his character was ever mentioned.
- That description doesn’t do it justice. It was the sort of comedy in the face of bureaucracy that only the British and Australians know how to do. If you’ve seen the “front fell off” video, that’s Clarke and Dawe.
In My Big Fat Greek Life, which was the TV show spun from My Big Fat Greek Wedding, the main character’s name was changed from Toula to Mia in an attempt to get some name recognition going with Nia Vardalos.
There’s Harry Anderson playing Harry Stone on Night Court.
Perfect.
Let’s formally eliminate actors on shows named for themselves. So Roseanne and Bob Newhart are out; Tony’s still in for Who’s the Boss?, and this one fits perfectly as wel;.
Vivian Vance in The Lucy Show (but not in I Love Lucy).
Charlie Sheen as Charlie Harper in Two and a Half Men.
I guess my link in post #8 was too subtle?
Not quite the same thing, but I just saw a late season episode of Hawaii Five-0 where character actor Kwan Hi Lim, who appeared dozens of times over the course of the show as a different character each time, played a judge. In the credits he was listed simply as “Judge,” but the placard on his bench read “Judge Kwan Hi Lim.”
He also played a con-man character named “Harry the Hat” on Cheers before that.
Tim Allen played Tim Taylor on Home Improvement.
Several of the supporting characters on The Office (US) are named after the actors: Phyllis, Angela, Oscar, and Creed are all played by actors with those same first names. For Creed both the character and the actor have the same full name: Creed Bratton.