The USCG does want to be notified when a Documented Vessel changes hands.
Technically the boats previous owner should have filed the paperwork with the USCG, indicating that they sold the vessel using the USCG Billing of Sale
(Form CG-1340), either the owner of the auction house, if it was repossessed.
You would then re-apply for documentation in your name on a USCG Form (CG-1258)
Since you purchased the boat at auction, I would guess you do not have a lien on the vessel. Many banks will require USCG Documentation over State Registration to secure the loan. Basically it makes it easier for the Bank to track and repossess the vessel., especially if it is out of country.
If you are considering traveling outside the USA with the boat, I would highly recommend Documenting it with the USCG, which currently is a one time fee and free renewals, although that may change soon. Foreign Ports
recognize USCG paperwork, but may not recognize State Registration forms.
Here is a link to the USCG Vessel Documentation Center's FAQ page, which should answer any further questions.