Am I Required To Tell My Old Psychiatrist The Name of My New One?

I switched practices recently because, on top of never responding to emails or phone calls, after my provider stopped working there they switched me to someone who felt extremely controlling and belittling. I messaged them in multiple places saying I found a new practice and they still reached out to me asking to make a new appointment. Now they're asking me the name of my new provider so they can "close the case." Sorry if this sounds rediculous, but I'm afraid of some sort of retaliation or badmouthing to my new psych. I just want them to leave me alone. Am I required to give that information? I'm in Florida. My worst nightmare is them sending someone to my home as a wellness check or something. Thanks.