How to identify clients on a server with the same IP?

Question

Nginx

There is an ordinary router in the local network with Internet access. If I'm not mistaken, all clients connected to the router receive the same IP (external) to access the network.
How then on the server side to identify each of the clients, according to what data (headers)?

Answer 1

Create a unique session cookie and identify it that way?

Answer 2

according to what data (headers)?

By no means, you need to implement an authentication mechanism .