DNS and DHCP for local and remote office. Where to put them and how to set up DNS to resolve all computer names?

Question

Domain Name System

Network:
There is a local office 10.0.1.0\24, RB951Ui router, 50 computers are gradually brought into the domain and one PC ala server (with AD, DNS)
There is a remote office 10.0.5.0\24, RB751U router, 10 computers without a domain (and I'm not going to them yet).
Offices are connected via openvpn, routes are registered and everything seems to be working.
How can I make sure that I have a single DNS namespace? So that a computer from any network could convert the name for any computer and that it was more or less reliable?
PS And where can I see the records on windows DNS that were created in the process of "dynamic DNS updates"?

Answer 1

If the vpn is stable, then in the remote office dhcp relay to the main dhcp server. Set up a service account on the dhcp server with membership in the dnsupdateproxy group

Answer 2

Configure DHCP as you like, the main thing is that everyone has different addresses and names, then it simply indicates a single DNS and that's it.
in the DNS on the server, everyone needs to check the box "allow those who passed the test to update the DNS address" (something like this)