I don't think you need to name the server "chat". But i haven't done this, so i'm only assuming. You can create a DNS entry (alias: pointing chat.contoso.com to servername (if the server's name is already resolvable by some other DNS record), or a record: pointing chat.contoso.com to IP address of the server). Then you can create a SRV record pointing queries to conto.com on 5222 to chat.contoso.com. This should get rid of a warning. Though, that warning is more like informational and things can work correctly even with it showing (in some cases, like in mine). Your fqdn can even be just chat. I don't think there is a requirement for it to replicate the main domain name. XMPP doesn't understand subdomaining. chat.contoso.com and contoso.com are two completely different domains for XMPP. Your users would need to put conto.com in their clients for login, so chat.contoso.com is not anywhere in that scheme.
I would try:
name server - chatserver
put chatserver as fqdn during setup
put conto.com as xmpp domain during setup
add A record pointing chatserver to its IP
add SRV record for queries to conto.com on 5222 to point to chatserver
It kept asking me to complete the setup because I forgot to restart openfire after moving the config files
Ok, I had everything running. I could even login to the new server (using IP instead of server name), but as soon as I swapped the IP address I was not able to login anymore.
The old server has multiple Virtual NICs, so maybe something is configure thru a different IP? I checked and everything seems to be configured thru server name, or localhost. So not sure.
For the moment, I swap it back (using old server for the weekend) but the new server does not work anymore. Weird.
I also made sure routing is right (I did have 1 problem there before, but it is fixed now)