You may use the name of the former salon as long as it is CLEAR that you are not claiming any affiliation with it. So, for example, you could say, "Grooming by John/Jane Doe, who formerly worker with That Other Salon."As you do this, 1) if you signed any agreements which would limit your ability to use the former salon's name, you must honor those agreements; and 2) you can't use the salon's trade or service mark, so don't use it's special font, logo, etc.--just list the name in regular type, the way you would on a resume.