In the past I have always tried to protect the best interests of my clients, and one of the items that I put on the top of my list, is helping them register their own domain name. Many web designers and webmasters, feel it is easier to assist clients by taking ownership of a clients domain name, and in the process add a bit of service fee for that service. I have always been worried that for if some reason I was ever incapacitated indefinitely, anyone can be run over by a bus. So I have always made a practice to help clients setup a domain name with a registrar and they also will pay the renewal fees. Your name is yours, why would want to lose it because of a complication in your web designer/masters life? You maybe concerned about the technical part of owning your domain name, but any person with technical experiencing including a new web designer/master should be able to help you change your settings to push your domain to the appropriate servers. You also now are in a position to change web designers/masters at any time without any obligation, unlike if someone else owns your name.
So the question to a lot of people is how likely is this really to be a concern? Well years ago when I first got into assisting clients with domains, one of my first clients, had a couple who ran a web design company and they unfortunately had started into a messy divorce, and not only had stopped talking to each other, but all their clients as well. There was definitely some struggles and we were able to resolve and move the ownership. Now we jump forward almost a decade later, and some other clients of mine had a web designer/master who became very very sick and kept hoping he was going to recover, but unfortunately he never was able to and passed away. The family had no technical knowledge and his record keeping was not the easiest to follow, and to add to things, he used different registrars here and there with different credentials. Some of his clients I am still struggling to find their domains names to help them move over to their own registrar. So if you think it can't happen, that is like thinking, your computer will never crash and you do not need a backup. Make good backups of your computer and also make sure you are the owner of your domain name, there is no need for your web designer/master to own your name.