Register Domain name if it is the same as your domain controller

I have a dc and a ts. my ts is part of the dc. the ts is also set up as a ftp server.

i have a company that hosts my email, we have a few domain names through them. if i register the domain name that i use for my dc, and have that domain point to my public, can i log into the ftp server using the domain name. If so, is it wise to use the domain name of my domain controller, if not, is there another way.

Also, i use cisco vpn client software. can i and/or how can i make my cisco router the same domain name so when i pass out cisco vpn installation discs, i can use the domain name to connect as opposed to using my public.