Dynamic DNS for home network

[Mate1999]

I have a small home network, there is a desktop that I use with windows remote desktop on iPad, laptop etc. I want the desktop to use the DHCP from Telstra NBN AP but resolve it to a domain name e.g. Desktop.local. The issue is that I don't want to use external DynDNS and the second problem is that I can't have the desktop running 24x7.

Is there a way in Telstra AP to define a local domain name map it to what-ever-IP it is given by DHCP and use it?  

[cf4 · Accepted solution]

Unfortunately there is no way to do this in the Telstra modem's

[Mate1999]

Thanks for your feedback