Re: "Snoopy characters"
The star - or the would-be star - is the show's unique selling point, so you name it after them, and not a snappy title that the audience is still less likely to remember. In some cases, "The Name Of Leading Performer Show" also has a different setting and even cast each week, aside from that one constant element. "Hancock's Half Hour" for instance didn't particularly start like that but ended up that way.
It's also a case where the star plays a character with the same name, which could confuse a stupid person and worries me - although with "Hancock", the show tended to be about what the cast of the show got up to when they weren't performing the show... except that that was, in fact, the show. Even more confusing. But it did make sense for Mr Tony Hancock to appear as Mr Tony Hancock.