There are numerous reasons to rebrand. Some are safety related, others are just good business. A name is the foundation of ones brand, it imparts a reaction and can be the difference between getting glory hole seekers/baskin-robbins types or genuine, long term bankable clients. The right name can give a provider more confidence and help change her perspective within the industry.
My clients would not be attracted to ads with someone named Cathy; Catherine however, denotes strength of character. An interesting aside, the men who attempt to call me Cathy are always boundary pusher and hagglers. I'm not sure what it means but if I open an email and he starts out trying to call me Cathy, we aren't going to meet because never once has it been a worthy experience for me; even if they are willing to pay my rates.
A solid business name makes establishing your desired business model easier. If an ethical provider is changing her name, there is an aspect of her business that she isn't happy with that elbow grease can't fix. Unethical providers change their name as often as they change their contact information. You can't compare the two, they are different in their entirety.
smiles, cat