To see if your desired domain name is available, do a domain check . By having your own domain name your website address and email addresses will be shorter and easier to remember. A website with its own domain name appears much more professional than one hosted under an ISP's domain. Yes, you must purchase a domain name if you do not already have one. Yes, of course.
Some web hosts register domains in their own name.
So essentially the web host owns your domain name and not you. This can cause a lot of problems. There is no charge to do this. In order for people from all over the world to view your webpages you need to have them located on a computer system that has a continuous high speed connection to the Internet. Servers, along with their high speed connections, are very expensive to purchase and maintain.