You can always leave your domain name with your current registrar or host if you wish to do so, and simply change the domain’s nameservers to point to your NEW host’s server.
Now, for those of you who DO wish to transfer your domain name away from your current registrar/host.
Can I change my host and keep my domain name?
Yes, of course its possible. You simply transfer your domain name to another hosting company. The issue is that most of the hosting companies will make it extremely difficult to transfer the domain name, while forcing you to stay with them. So you should expect the downtime most likely.
How do I move my website from one host to another?
The most convenient way to transfer your website’s files to your new web hosting account is via FTP. You should connect to your hosting account and download the files locally to your computer. Then you have to upload them to your new hosting account’s main folder (usually public_html, www or httpdocs).
Can I transfer my GoDaddy domain to another host?
You can transfer your domain to GoDaddy from another registrar. You’ll need to prepare your domain name at your current registrar before completing the steps with GoDaddy. If your domain is already registered with GoDaddy, you can move your domain to another GoDaddy account.
Can I transfer a domain name from one registrar to another?
It is your right to transfer your domain name registration between registrars. If you wish to move your domain name from one ICANN -accredited registrar to another, you may initiate the transfer process by contacting the registrar to which you wish to transfer the name.