DNS for NAT'd domain with dynamic IP

My firewall is in place and working properly where I have a DMZ and internal LAN. I have a domain registered with namecheap.com and have a dynamic IP. Right now I have the servers running with a hostname of mail.my.domain and dns.my.domain and http://www.my.domain in the DMZ.

How do i setup DNS so internally I can access mail.myname.com or http://www.myname.com from both the Internet and internally? Internally I can type the IP of http://www.myname.com and go there, but that isn't what I want.

namecheap.com is the registrar and I'm using their nameservers, so I only want DNS locally.
 
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