Well, it's a hostname, not a URL. Yes, you'd need to register each hostname you want to use (mail., www., ftp., etc.), and zoneedit is where you'd do that. As of a few minutes ago, zoneedit's nameservers didn't recognize mail.securechoice.net:
[dan@e-smith dan]$ nslookup mail.securechoice.net 207.228.252.101
Server: ns1.zoneedit.com
Address: 207.228.252.101
*** ns1.zoneedit.com can't find mail.securechoice.net: Non-existent host/domain