I think most dommes starting out don't plan on a long term career. Heaven only knows that when I started out to pay for law school "Mistress Morgan" would have been taken and really popular when I arrived in Los Angeles in 2000. I thought shortening it to one letter was cool and literary like JD Salinger, ee cummings, TS Elliot, ect. I wasn't thinking it would end up being a little generic and not work for google searches and I would then be confused with Mistress M in San Diego, Empress M in Connecticut, Lady M in New York, and so on.

Most of us start out as dabbling as a pro and rarely have a global strategy spanning 10+ years. I doubt most dommes are thinking of riding someone else's coattails by "stealing" their name. (That may happen, but it is not the norm.) I am pretty sure most every domme is thinking they are going to have some fun and pick up some extra money.
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I've broken all my toys. Would you like to be broken?