The host name is established through the domain name service (DNS). If you want your client to have a host name, your client will need a DNS listing. If that's what you want to pursue, you might want to look at other questions on DNS either on this site or on the ServerFault or SuperUser site.
If you just want a client identifier for the convenience of your system, you can send it over the connection after the connection is established, using a protocol - that is, a communications format - that you establish for both client and server. For example, your client could send a serialized java.lang.String containing its name to the server as the first thing it does on the connection. Your server could then read the name from connection after it is established.