Registration of an existing firearm as an SBR/SBS is done on the BATFE form 1.
https://www.atf.gov/file/11281/download
The difference between an individual and a trust is which box is checked in section #2, and filling out #11-14 if registering as an individual. Reading the instructions on the linked form (easy) and trying to understand what it means (not as easy?) will give you a good base for asking further specific questions.
If your dealer doesn't know how to help an individual submit the form, I would be very wary about using them for anything. If you would state where you live, you might get some recommendations for better dealers.
With all the access restrictions that come with NFA items, and the additional access restrictions that come with registering an item to an individual, are you sure you don't want to do a trust?
The usual qualifiers apply: I'm not a lawyer, not an expert, ymmv...