How to push a local DNS resolving entry to client when an OpenVPN connection established?

I am using OpenVPN-2.4.6 clients and an OpenVPN-2.4.5 server that resides an OpenWRT(18.06.01) router.

The OVPN client connects to the server by a public DNS name of the server(i.e pubName.my.router), instead of an ip since the ip of the server is dynamic.

Can I(and how to) add a local domain entry of the server(i.e privateName.in.vpn) to the resolver of the clients?

Because OpenVPN would resolve and cache the ip of pubName.my.router before it starts connecting, I believe that the local entry added later will not disturb the traffic of OVPN own.

Basically, I think I have three questions:

1. I'm prefer to do in a manner come with OVPN, if any(But I didn't found it).
2. If it can not be done with OVPN, how to add such an entry into my local resolver(of a linux box)?
3. What is the kind of the resolver of my Kubuntu box by default(So I can search more documents)?

Any suggestions or hints will be appreciated! Pls mercy a Chinese writing such an ugly English post, I wish I have expressed things correctly. Thank you anyway!