It really depends on the company that you use to manage the domain's DNS. As long as they have an API to update DNS records..

For example, I can have my domain at Porkbun and have its DNS managed at Cloudflare. Cloudflare allows updating DNS records via API..so there's programs to update it. Some routers even support it.

Worst case, you can set up a service like duckdns and have your domain, via cname, point to the duck DNS subdomain.

There's options.

There are many ways to update dns automatically, I have used this container in the past. You could probably even write a bash script/cron job that checks your IP and updates it with curl depending on your DNS provider.

If you are already running tailscale you may be interested in using a funnel, which lets you accept and route internet traffic to your tailnet. I don't use tailscale so can't comment on how good/bad/useful this is.

You could also run some sort of service like frp from some remote box (like a VPS in DO/Linode/etc). This or the funnel lets you not expose/advertise your home IP address if that is a consideration.

All domains works with Dynamic IPs - it all depends on what DNS-provider you use :) Provider like Cloudflare ( I do not recommend Cloudflare) and afraid.org both offer dynamic DNS.

Cloudflare, Porkbun, Namecheap and many other registrars offer dynamic DNS via API or a ddns client very easy to setup.

CloudFlare ZT tunnels coupled with an Azure AD. Work’s amazingly with their containers to keep the tunnel alive.

Does your ISP support IPv6?

ZoneEdit.com has a free plan with dynamic DNS for at least one „real“ domain (domain registration not included). It‘s not the most user friendly UI but super powerful. You can pretty much add any DNS record you like.

Do you want the host to be accessible fully from any host, or do you control all hosts you want to access it?

For mine, all the devices I want to access my personal host I have setup zerotier, and then pointed cloudflare at my zerotier address.

Any device I want to access my host (outside of my local network) requires zerotier.

I don’t want anything outside of my control accessing my host

I used No-IP for this very thing many years ago (using a domain on a server with a dynamic IP, anyway). I don't know how it is now, but a quick search shows it is still around.