I considered a few other names. My real name Rex (actually Rexford) has a feminine form of Regina. That could be shortened to Reggie, but that still sounds to masculine, or Gina, which sounded too much like a drag queen name to me. My other concern was that I wanted to be able to talk about my feminine side without having men wanting me to introduce them. Names like Gloria, or more exotic names would be harder to ignore and easier to associate.
I had had several women friends named Debbie, (Deborah actually), and I associated that name with fun, playfulness, and just a joy of life, because of my friends. These were women I wanted to emulate. My sponsor said "Like Debutante?", which almost made me think about another choice, but I realized it was a good name for "Coming out".
The last name "Lawrence" is my mother's mother's mother's maiden name, and after her husband left her in Missouri, she homesteaded in Montana with her sister, where women could own land. She then went to Central City where she realized that she could become very rich selling baths to miners and doing laundry for the saloon girls. Particularly relevant was that she had to wear a skirt over her pants when she went into town, because women who wore pants into town were often tarred, feathered, and rode out of town on a rail. It looked funny at the time, but most people died a horrible death within a week or two afterward.