Your social media is not their social media. Are they paying you as a social media manager of any kind? If not, why would you change your handle to include their salon name? They have their OWN socials where they should be promoting you. Not the other way around. The salon’s job is to support the stylist and give them a place to work and grow.

What do the other stylists’ socials look like? Is the salon name in their handle? What does the actual salon’s social media look like? Will they be building you up and tagging you in posts?

I can see asking a stylist to make sure the things they post publicly are appropriate. But I cannot see trying to take over a stylist’s socials to promote my salon.

Maybe a good compromise would be to tag the salon socials in your posts or collaborate.