Yes.
Some website administrators think it's a good idea to keep the hosting part and the domain part separate. However, it is really a question of how you feel about the integrity of the hosting and domain services offered to you.
Now if you can use your imagination, imagine this situation where the same company could offer you both medical services and legal services. Thus your doctor will be working for the same company as your lawyer. Of course, in real life that could never happen, that would be a huge conflict of interest.
A domain name for your website is not very costly at all. Typically about $12 a year. Your web hosting costs could vary widely, any where from a few dollars a year up into the hundreds or even thousands of dollars. People remember your website by the
domain name. They have almost no idea about who the hosting company is.
Your domain name becomes your reputation. In time your domain name and its reputation become the most valuable asset you have. If your hosting service is not able to satisfy your needs, even switch the name servers in your domain account to another web hosting service. So one of the things you'll be interested in is how easy is it to change the name servers for your domain name. Having a domain registrar that is very honest and has the highest integrity would be very important to you.
Let me get to the point. If you had a dispute with year domain registrar it should be easy to resolve the issue. After all, you're only paying a few dollars a year for the domain name so there should not be any dispute about share ownership of the domain name. The registrar only makes a small amount from registering your domain for every year.
The web hosting service is another issue. If there is any way he can take hold of your website it would be through the domain name. You can make backups of all the materialon the website and the web hosting service cannot use that material without violating copyright laws. However, if there is some way for him to obtain the domain name he could make things very difficult for you and enjoy the use of your website for his own gain. Do you see now how that could be a conflict between the registrar and the hosting service?
Of course, this does not apply if you really are certain about the integrity of the company you have chosen. But bear in mind you are dealing with two different services under one company. Now that's not always a bad idea, but in some cases it presents a conflict of interest for the domain registrar and hosting service to be the same company. At the present time there are no laws or accepted standards to prevent the hosting service to also offer domain registrar service.
The reason I get kind of hot about this issue is because I have been stung badly. Because of a dispute over a hosting service, my domain registrar stroll my domain names. To me these domain names had some value other than the money I paid to him for the registration service. But because I had a dispute with him over a hosting service, he proceeded to take my domain names because of my refusal to pay for a service that I did not order. That particular company is no longer in business. That is not much consolation to me, I lost the intellectual value of the domain names that I had carefully chosen.
So, now you know why I have this idea about keeping the two services separate. It is very unlikely that anything like that would ever happen again to someone like yourself. You seem to be a person that is very cautious and very careful, so you would probably not make the same mistake I did.
By the way, I did this from dictation because I have a handicap and I can't
catch all the typos and errors I might make.