Wait ok I’m not done with transfem!Greg (or Egg!greg cause I think I’m funny).
I think she decides to stick with a “G” name and makes a joke a long the lines of “Well I had to keep my monogram towel” (She does not nor would she ever be caught dead having monogram towels.)
Based on her age, I’m thinking Genevieve. Maybe there is an episode where she tries going by “Genni” and everyone is like trying to find a way to tell her that they hate it. Rebecca slips up and says something by accident at first but Genevieve says she can take it so it turns into a whole rant. They’re both doubled over laughing by the end. Rebecca purposes “Gen” as an alternative (she says Genevieve needs a single syllable name.) Gen repeats it a few times and agrees. AND THAT would be the perfect segues into “Hello, nice to meet you.” (Which I think would be so much cuter in this context!)
