My webmail is associated with local ip address
When people write "local IP address" they usually mean one of two things:
- The IP-address of the main network interface of a personal computer.
- The IP-address of a server (a different computer) on the local network.
It is unusual to run a mail service on a personal desktop or notebook computer. If you have a separate mail-server, whoever set that up will know it's name.
To configure it with gmail, I need to find the server name.
That would be unusual. Usually you can use a public IP-address anywhere you can use a name (specifically a DNS fully qualified hostname).
Is there a way to find server name?
You can try a reverse-DNS lookup.
C:\>nslookup 10.0.0.16 Server: myLocalNatRouter Address: 10.0.0.252 Name: myLocalMailServer Address: 10.0.0.16
If the webmail server is behind a NAT router or firewall, you will need for port-forwarding to be configured. Once you (or a helper) understand that, you'll know what name to give gmail.