I have a setup where the initial dns setup was given aa.com as the domain
and now I wish to change that to the correct host of befast.com

The problem is, the internal host/server is all.befast.com but the
www.befast.com is hosted on an isp's website.

How does one change the FQDN and allow the internal users who use the
dns/dhcp to access both all.befast.com, which is internal and the
www.befast.com which is hosted on the isp website?

Also, how does one change the aa.com to the befast.com after the dns has
been setup?