I’m with Karin on this one. Assuming you are an employee, not an independent contractor,then your employer (i.e.the studio owner) should provide insurance. As a safeguard, you probably should have professional liability insurance but that is an issue to discuss with your insurance agent. If you are working as an independent contractor,the studio owner is not your employer, but is contracting your services, therefore the owner may require that the business (i.e.the studio) be listed under your insurance for liability purposes. This is a reasonable and legitimate request to protect the interests of the studio owner.