There a lot of free subdomain providers out there with non-chanchable nameservers.
For a own article on subdomains, see here.
But if you use one of these provides, you cannot chanche their nameservers and you lose a lot of controls and features
that are avaliable on non-subdomains.
(Note: Technically, what you can get using this tutorial, actually isn't a real domain, but it's on the
public suffix list, so you can
connect it to your favourite DNS-provider, e.g. Cloudflare.)
And, well, it's free.