I use to but I don't any more for my customer's protection. Being a sole proprietor since the domain would be in my account if I passed away it would cause the domain not to get renewed and the customer would risk loosing it or paying a lot of money to get it into their name. For that reason I no longer register domain names for customers and have been getting existing domains transferred over to the business owner.
You can register your domain through any domain registrar and I can still host your website. It just requires pointing your domain to my hosting which I can walk you through over the phone.
I recommend GoDaddy
since I'm already with them which makes things real easy and they provide excellent support if you ever need it.
Note: If you create an account and register a domain through GoDaddy but want me to host your website, DO NOT buy a hosting plan.