I got a homelab, at the moment I am only running some local stuff and tailscale to reach my stuff remotely.
I can use tailscales ddns, but I would like a real domain. Is there a domain registrator that works with dynamic ips? Or do I need to use a CNAME instead of A record?
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.
I think using the cloudflare API is the way to go.
You could probably set up an internal service that translates your home router's dyndns request to a cloudflare API call.
Only if you had root access to your router. It’s a lot easier to write or find a very simple update script and schedule it to run every now and then via crontab.