The U.S. Coast Guard has a website - under the Department of Transportation (it''s like a mil.gov site) that you can find with a search. That information will cost you about $4 and they''ll bill you for it. They send the info via email, as I recall.
You can try sending a note to the agency that registers boats for that state and see if they will give you the owner''s name. I have gotten the name of an owner for a friend who backed into a boat while docking and wanted to contact the owner. Also if the boat is in a marina you may be able to get the owners name from the marina staff.