You can never know who own those coin , Unless he use the address bought something from you
Technically you can never prove who owns the coins in any case. You can only have an idea of who had access to that particular address at a given time. Addresses can transfer between people, be accessed by multiple people etc.
If you control a node that first received a TX from a particular address then you can see the IP address of the person who broadcast a TX.
It would be a huge security risk to share a single BTC address
