You need to clear this a bit.
If you have VPN then your MySQL looks like another machine in your network..
For example if your IPs are in the range of 192.168.1.1-192.168.1.100 your mySQL would appear as 192.168.1.101 is just a matter of the VPN connection and your network configuration.
Other than that you can connect either using its IP or its Name e.g. TonysMySQL
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