About setting a stable host name for the computer
In order to set up a VNC or RDP connection, you have to specify the server address, either it is an IP address or a host name. In most cases, users of Internet have a dynamic IP that change every time you relaunch your internet connection. In addition, ISP often assign one IP address to several users. These things make it impossible to connect directly to your computer from outside the local network.
To overcome this, you can use a Dynamic DNS service. When you are registered as a DDNS user, a special software running on your computer or router keeps it available by a static host name. For more information, see Dynamic DNS.
Many home networking routers support several DDNS providers out of the box. To see if your router supports it, check your router documentation.
A list of free Dynamic DNS service providers is available at DDNS — Free Dynamic DNS Providers.
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