Even if you transfer it to a trust, the individual owner’s name will be available to someone who’s looking for the individual because the transfer and prior owner’s information will be public.
Might want to talk to an attorney or talk to someone in public records. The best way to keep your name out of public records would be to never have the property in your name at all. Not sure that’s possible if you have a recorded mortgage of any kind, as most lenders require everything to be in your personal name.