There are two options here, depending on your setup:
If your machine is using DHCP to get an IP from the router, it is possible that the router is taking the hostname from the DHCP request and filling its internal DNS with that. In this case you have to release and obtain again an IP from the router. You can accomplish this by reconfiguring the interface (wlan0, eth0). Unluckily I don't know what tools LinuxMint uses for reconfiguring the interfaces, so you will have to figure it out by yourself.
The other option is that the router's internal DNS is filled by configuration, either from the DHCP section or from a dedicated DNS section. Check your router's configuration. I don't know the model you mention either, but it is possible that you will have to reboot the router.