The fact of the matter is that it is perfectly legal for your employer to terminate your employment for this. In an "at will" employment arrangement an employee can choose whether or not to work for a specific employer. Conversely, an employer can decide whether to hire or fire an employee, and just what the terms of employment will be. Therefore an employer can discharge an employee for any, or even no, reason. And it can do so with or without notice. Note:  Under certain conditions an employee would have protection. For instance, if such dismissal would violate specific company policy or the terms of a union/employment contract. Additionally, discrimination must play a factor in termination.So if you want to protect your job, either give up your recording company or use a a different name in the music business and/or have someone else front for you.