Generally an individual has the exclusive right to license the use of their identity for commercial purposes. If another person or company uses your likeness, name, or other recognizable aspects of your identity without your permission, they may be violating your rights. Only about half the states recognize the Right of Publicity. Many of these states put the right into statutes concerning either the Right to Privacy or under laws prohibiting unfair competition (concerning attempts to pass off a product as being endorsed by a certain individual).
If a person is able to trademark a certain aspect of their identity, it can be protected under federal law. The advantage of this is that your Right of Publicity for the trademarked aspect of your persona is protected no matter what state you are in.
In many places, unauthorized use or appropriation of a person’s name or likeness by another person or company means the person may be able to bring a lawsuit against the unauthorized user to stop them and possibly recover money damages. If you feel your identity has been used wrongfully without your permission, you can consult a business attorney to learn about your rights and whether you can take any action against the person or company using your identity without your permission.