Every website has a name not doubt about that. Its the name that you put in between www and com in your website address. Actually, with your websites name your website will also be designated an address that will be comprised of numbers, commonly known as the IP address. Both types of designations will identify your websites location, only that the web hosting name (the first type) is much easier to remember.
Whenever you sign up for a web hosting site, you are asked for a particular name that you would want your website to have. Of course, each web address must be unique, so theres a chance that the one you thought up of will not be available to you anymore because its already been taken, especially if the name you thought of is very common.
But if you already have a domain name, you have to specify that with your new web hosting site as well so that the proper arrangement can be made to fully transfer your existing website to their servers.
All in all, its very important that you deal with the name, above many other things, if you plan on building a website.