From a branding perspective it is wise to craft an identity that cannot be confused with other Dommes when starting out. A Domme seeking to create a recognizable brand, should definitely look up their desired name and check if there is already someone who has established a presence with said name. If so, the best way to create a separate lane of one's own (esp. as the BDSM sphere grows online) is definitely to have a name + last name combo.