At time of sale the owner should have provided a bill of sale and either an executed transfer of title [state] by signing on the title document, or an executed transfer of
documentation by signing on the back of the USCG certificate of title.
The title or documentation certificate should have thence been promptly returned to the State or the USCG.
The Title or the certificate of USCG documentation list the
ownership of the vessel.
There also may be liens recorded on the vessel which will need to be cleared before title or documentation can be transferred by the State or the USCG.
Is your vessel free of liens? If not then you will need to pursue release of any and all liens.
Obtain the original Title or the original USCG certificate of documentation from the seller, and follow the instructions as to how to have executed the recordation of the sale.
There is need for the owner's execution of transfer via the Title document or the certificate of documentation to be notarized.
"A couple of months have passed" which means you are tardy in processing the
ownership transfer. The law requires prompt recordation of change of ownership, get on with it.