First episode: December 5, 1951
    Bill's first episode: August 6, 1952?
    Bill's last episode: January 20, 1953
Last episode: October 7, 1955
A celebrity panel asks yes or no questions trying to identify the unusual names of the guests.

Bill is never listed as a regular for this series, but early in his career, as he was beginning to make a name for himself on I've Got A Secret, he made at least six consecutive appearances as a panelist from August 6 to September 10, 1952, and two more appearances a few months later.  It's possible his appearances on this show may have started before August, 1952, but that episode appears to be the earliest surviving episode for the series.  He was probably only a replacement for Meredith Willson during that time, but the regularity of his appearances warrant at least a mention on this site.

Many, maybe even all of Bill's appearances on The Name's The Same survive, as does much of the entire series.  The series has been seen on GSN: The Network For Games as recently as 2008 as part of their Black & White Overnight block.
Watch Bill question a youngster named "Bill Cullen":  

Our own The Name's the Same episode guide for the entire series
The Name's the Same page at Adam Nedeff's Bill Cullen's World
The Name's The Same page at Tim's TV Showcase
The Name's The Same page on Wikipedia
Theme music copyright information at David Shields' site for Classic TV Themes