Proof of ownership is an important part of this process. If you don't have receipts, your bike shop or online dealer will be able to look you up. My local bike shop keeps a record of everything I buy. It's great, because if I have a problem I don't ever need a receipt--they just look up the purchase and then help me with my problem. And, the dealer where I bought my bike? They all know me, so that would be easy peasy.
If you got the bike second-hand, the original purchaser can be helpful.
If it turns out you purchased a stolen bike and you discover that through this process, take the bike to the police in your area so that they can return it to the owner. Expensive lesson learned.