This is a revised version of the test pilot. About half of the footage shown as the pilot is reused, only adding new footage where different actors are playing different parts.
Ann Marie's agent suggests she change her name because it "sounds unfinished" ("Ann Marie what?" He quipped). He suggests that she'll never be a star with a name that sounds like only a first name. However, this was clearly fiction because in real life, the actor Rose Marie was very well-known and a star. (Rose Marie was a recurring cast member of The Dick Van Dyke show, which appeared years before That Girl.)
The title is from a quote from the Shakespeare play Romeo and Juliet: "What's in a name. That which we call a rose, By any other name would smell as sweet."