Thanks for your reply, and sorry if I misunderstand a bit or if I don't use the rights words, english is not my mother tongue.
By "linking the host name to the internal server IP address", I was referring to a A record.
So, I'm getting a bit further in my understanding of the DNS setup.
I just have another question. I have a A record in my DNS provider like this : subdomain.domain.com IN A 82.229.XXX.XXX, which is my router IP address.
I wonder if it's possible to use this subdomain as the host name of my mac server, and also my internal name server ?
When I try this, with my hostname and primary zone being subdomain.domain.com (plus A record and PTR on private IP), the DNS setup seems to work correctly (cmd host with hostname and private IP, displayed public host name in server.app, dig, changeip etc), but I am not able to use remote services such as Contacts on a device not connected to the local network. It says that credentials are not valid when I try to log in on my iPhone for example (but they should be). And I can only use network file sharing with afp, smb won't work.
But, if I use a host name before the subdomain, such as server.subdomain.domain.com, with subdomain.domain.com as primary zone, then everything works, lan filesharing, VPN, Contacts, cal etc, except that there's no public host name in the internet reachability, only my router IP address.
So, what am I missing ? I am bit confused by the fact that, in the first case, everything seems to be ok but is clearly not, and in the second case, it doesn't seem to be perfectly set up, but things work...