As we frequently advise customers it is always best to keep services in contracts you control. This applies equally to your domain name. Never have this registered in a name other than your own, it is easy to do and a number of reliable domain registrars exist.
Domain names are extremely important to any business and can be a valuable asset to your company. The loss of a domain name, or a temporary loss of access, can result in the closure of your website as easily as any disgruntled host. It is always recommended to register your own domain, and then employ the services of a host, and point said domain to the aforementioned host.
If a host has set up and registered your domain name, they not only have all your data but also your e-commerce web address. Now imagine if something went wrong with your relationship with said developer, by withholding your domain name they effectively close you site, and prevent you from reopening with a new host. You may be able to prove ownership of a domain name but this can be a very lengthy process resulting in the loss of Google ranking and the loss of customers past and present.
Equally important, do not use the same password for host and domain name and never leave passwords set to anything generic. As difficult as randomly generated passwords are to remember they are also extremely difficult for others to guess. Passwords such as your name, your shop name, admin etc. are easy to remember and very easy for others to break. You do not want someone gaining access to your online shop, even with backups you will face down time and often this will be targeted at the busiest period for sales.
You want to be in control of your own business. By paying directly to a domain registrar, an unrelated host and then a web designer you restrict everyone’s access to your store and not the other way around.
Essentially when you decide upon a website/e-commerce site the rules to follow are:
Register your own domain name.
Employ the services of a host.
Point your domain name to said host.
Employ if needed, a web designer.
Remember, you should control access to your site. By paying for each service directly you limit any potential issues you may face.