How to connect to Microsoft Windows machine using host name only via Microsoft Remote Desktop
Your best bet is to set up a static DHCP lease in your router and specify the host name.

Since you are using a home network, I am going under the assumption you are using a consumer grade "router" to connect to the Internet.  It's also your DHCP server, your DNS server (repeater), and your WiFi access point.

Somewhere in your router's setup, there is an option for static DHCP leases.  What you do is take the MAC address of your Windows machine, pick an IP address (I like to go outside the pool) and make an entry for a lease.  You can enter a hostname here as well.

The static lease means your device still get's its IP via DHCP, but the DHCP server will always hand out the same IP when requested.  Once you do that, it will cache the DNS host name.  So, from any computer on your home network, you will be able to connect to it.