Depends where you live
Where do you live? If it's in one of the "gun-friendlier" states, like VA where I live. There IS no gun registration, so there's no way to check.
If you live in CA, you might need to have it transferred to you through an FFL 01 holder or something like that.
Simple thing to do here if you live in a state like VA is to just ask the relative to sign a reciept saying the gun with SN such and such was given to you on such and such a date. However, I don't see this as a major issue and probably wouldn't really bother with it. Enjoy your gift. There's no need to tell the gov. what you have when it's not required by law.