That form (4473) that you filled out at purchase traces the gun to you as the original buyer, assuming it was a new gun at the time. When guns are recovered by any form of police a check is started. It goes from the mfr to the distributor to the store that sold it. The store looks up who they sold it to and you get a call.
Note for future reference: if you lose a gun, file a police report even if you can’t describe it completely. Note also that, in your case, Ruger has always serialized their guns so that if you buy one new, it will always trace to you. FWIW that whole tracing operation rarely takes more than a day. Some states have a law requiring reporting missing guns. Failing that can get you a nasty phone call.
No worries there. I definitely report any such thefts. It’s only happened once and ever since that boat trip I have no more worries on that score.