A domain registration designates ownership of the name of your website and can be purchased from any company you like. You can then choose to host the website at the same company, or choose to host at a different company by pointing its DNS records.
While you do not need to have your registration at the same company that you are hosting the site, it makes it easier to manage your website as you can control all of the details from the same location. The following articles explain how to transfer your registration to, or away from, DreamHost:
You can also transfer between two different DreamHost accounts:
When transferring a registration, it's possible that it will fail to complete. There are several reasons this can occur, and the following article explains a few of these reasons and how to proceed:
ICANN transfer policy
ICANN policy states that if you change any of the WHOIS information for your domain, it is then locked for 60 days, preventing you from transferring it. However, you can opt-out of the restriction in the DreamHost panel. View the following article for further details: