Hosting provides the publishing area . Hosting provides a URL (Uniform Resource Locator, or "website address") for your newly created website.
A web address may be similar to: A "domain" URL www.yourname.com can be purchased.
You should buy your own domain name, try to avoid domain transfter and legal problems in future.
Check availability of a domain name or see your domain name creation date .
Generally domain registry takes 2 business day set up.
Your website maintenance and updates can be done by your webmaster , a web designer or even by yourself.
I do regular maintenance work for my clients.
Domain name Registration Fee:
It usually depends on the name ending .com or .biz price vary between $10.00 to $20.00 if that domain name is not registered before.
You can also transfer to existing domain name to your new hosting place and that takes usually 7 - 10 days for DNS registry complete.
1and1 Hosting Company:
Depends on how much place you need, many packages available at 1and1.com website.
Please read more information about 1and1 hosting and domain payments here.