Thanks so far for your help.
I'll explain our dns setup and maybe you can provide some advice on what I should do.
Our DNS server (in the DMZ as well) handles 1 zone (domain.example)
records in our zone file are as follows...
www IN A 18.104.22.168
ns1 IN A 22.214.171.124
mail IN A 126.96.36.199
@ IN A 188.8.131.52
domain.example. MX 1 mail
As you can see, all the hosts resolve to the same IP address. Because everything is behind that address in the dmz.
These DMZ servers (we have a few) all use our ISP's nameservers to resolve queries.
I'm confused as to what proper hostname I should be assigning to these computers, specifically this new mail server. It seems like whatever hostname I assign, none of them will resolve (in the zimbra setup)