Terminal. Strange name in TERMINAL

Which name is the one that you don't recognize?

The one before the "~" symbol is the computer's name from System Preferences - Sharing. You can change it and then reboot to take effect.

The one before the "$" symbol is your user short name.

Matt

sudo scutil --set HostName whatever-you-want

If that doesn't work, the hostname is being set to the result of a reverse lookup of your IP address on a local DNS server, most likely your gateway.