Third level domain name for internal VM

Is it possible to use a third level domain name for an internal server?

I am working on a web project with an external prod server (a VPS hosted on Linode running Ubuntu) which uses it own domain (eg accessible as www.mydomain.com and mydomain.com).

And I have setup an internal VM running Ubuntu as my test server (on my home network). This has the same setup as prod except the domain and machine names. They are running Nginx as the web server (actually setup as a reverse proxy).

I would like to setup the internal VM so the web app can be accessed via test.mydomain.com - just not sure if it's possible (as the second level domain name is externally defined)... and if so, how? Ie do I need to spin up a DNS server or can I use a hosts file and do I need to do any config on Nginx etc?

Thanks