You'll need a DNS server that you can manage. Then you'd have to add a new domain to your forward lookup zones.
ie http://customurl.com to 192.168.1.1
Then on the MX as @MRCUR specified you can change the DNS server in the DHCP settings to point to the DNS server that you can manage above.
Adam R MS | CISSP, CISM, VCP, MCITP, CCNP, ITILv3, CMNO
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