If I leave the name blank I get the error message "CNAME records may only be used on sub-domains."
If I use "www" I instead get the error message "You already have a record for this name. You can't have a CNAME and any other record on the same name."
The current value is [mydomain].cdn.cloudflare.net, but that record along with a bunch of others are listed under the heading Non-editable DreamHost DNS records.
EDIT: Thanks for the quick replies patricktan and Andrew F.
Removing the hosting, would that not remove my email addresses?