Do you... really care if someone outside you network knows the domain you chose for an internal network service?

That's not sensitive information. Also, there's basically no way for cloudflare, even if they were being malicious about it, to collect and use that information. What would they do with it?

Yes, I care. Why don't you? I work for Tier 1 banks. They are paranoid, and rightly so. One of their many paranoid rules is that hostnames can never betray the machine's purpose. You could easily analyze DoH stats and deduce certain machines' functions.

Leaking information is bad.

It's definitely sensitive information --- useful for attackers to find out the structure of the LAN.