I have promoted my social media handles extensively. Do I have any rights in my social media handles?

You have rights in the content posted on the social media handles. The primary rights to your social media handles rest with the platform hosting your handle. The platform reserves the right to delete your account in the event of infringement or violation of the law of the land.

Having said that, if you promote your social media handle (or your name) extensively, it may be considered a brand name in itself, and that could allow you to protect your social media handle (or your name) as a trademark.