When you hire someone for your web site, or even if that person is doing your site for free as a favor, YOU should buy the domain name and YOU should buy the hosting service. And actually any email add-ons you may need too.
The reason I mention this is we have spend the past few months tracking down the ownership of a domain name that was purchased for a client by a friend and that friend subsequently moved away. Which means we could not move the domain to another hosting service. Trapped.
Are you lost?
When you set up a web site there are two parts...
The Domain. The URL. The Dot Com.
There are big name servers in the sky, and way less of them than you would guess, who take the "www" addresses we type in and based on settings, they know what specific server to send us to, so the right web site appears in our browser. Ownership of this name means just that. You have purchased the right to have www.whatever.com for a specified period and you get to do what you want with it. Domain name ownership should cost about $10-15 per year or less, depending on what you get.
Hosting Service For Your Files. The ISP (Internet Service Provider).
This is a company that provides space on their servers and hopefully an easy dashboard of some kind to mange your accounts. Because you will put your web site files here and tell those aforementioned name servers where your stuff is. This is the place you make edits to your site, whether directly to the files or via a content management system (CMS) like Wordpress. Hosting should cost between $5-15 per month depending on your needs and the size of your site. When looking to buy into a service, reputation and stability matters. Also be sure you are purchasing a plan that covers your needs. Like the ability to install Wordpress, or maybe you need add-on email service (usually $2-5 per month).
But the real crux of this post is YOU need to own these accounts.
If you are talking to a possible web designer and they want to put these things on THEIR account, I am not suggesting they are bad news, but you are not protecting your site by allowing that.
In the case of my client, his friend could have (literally) redirected their site at any time to his hosting plan and put whatever up on site he wanted. Luckily, the friend is a good guy and we just had to track him down... and all is well.
The way to work with a web developer in these cases is for you to buy the domains and hosting accounts and give your designer ACCESS. We DO need that. And they can even help you set up your domain and hosting, as I have done for clients, but not to belabor the point, the accounts remain with the client.
For safety's sake, it's a good idea to give your designer a separate admin account that can be removed when the work is done, or, at the very least... change the passwords afterwards... IF they are accessing via your log-ins.
Hate to sound all Chicken Little, but trust me on this one.