After seeing kawliga’s answer of Kramer vs. Kramer I immediately thought of Bonnie & Clyde, with Warren Beatty and Faye Dunnaway. But not being sure, I (cheated and) looked it up on the IMDB, and no, not only did the film not win Best Picture but neither star won, either.
So now you’ve got me curious enough to actually find out the answer. Is it NOT cheating if we look things up on sites other than the IMDB?
I went to the official Acadamy site (www.oscars.com) and you can easily look up past winners, decade by decade in any category.
While there are quite a few Best picture Winners that have character’s names in the title, there are none with TWO character names in the title, except for Kramer vs. Kramer.
Maybe I don’t really understand the question… What is a "title character "?
Thinking there might be a trick or surprise or what have you, upon further investigation I have learned that of all the Best Picture Winners which have character names in the title, only four have two winners in the acting categories.
(Wait: is that the trick? Do you consider a “Performance Oscar” something other than Best Actor, Best Actress, Best Supporting Actor or Best Supporting Actress?)
The four are:
Kramer vs. Kramer (1979) with Dustin Hoffman winning Best Actor and Meryl Streep winning Best Supporting Actress
Shakespeare In Love (1998) with Gwyneth Paltrow Best Actress and Judi Dench Best Supporting Actress
Ben Hur (1959) with Charleton Heston Best Actor and Hugh Griffith Best Supporting Actor
Mrs. Minniver (1942) with Greer Garson Best Actress and Teresa Wright Best Supporting Actress
(And neither Shakespeare winner played Shakespeare!)
Am I missing something?
Here’s a guess: Do both Greer Garson and Teresa Wright play “Mrs. Miniver” at different ages? Nope (IMDB again).
OK… I give up… 
(BTW, I see that I was right: Lee Marvin did win best actor for Cat Ballou, which I just know he played his own brother (one a bad gunslinger and the other his drunk brother with the metal nose… or is it the bad one with the silver nose?), and I didn’t look that one up first!
)