So you want a self hosted wordpress blog ? hmm that’s a good idea. It’s always good to own a little piece of web for yourself.
First, you should get a domain name. Yes, think hard, and select a domain name. But, keep domain registrar’s website open while you are doing this serious thinking. Because, you need to make sure that the domain that you want to register, is actually available. You can’t register someone Else’s domain name 
You can use any of the following checkdomain.com register.com godaddy.com So, when there is a domain name ready, you can register it.
Tip: Do not register the domain straightaway , if you are planning to buy hosting for 1 year, or 2 years, most of the webhosts give you a free domain name with the hosting plan, you can make use of this offer.
It is okay to have the domain name registered with one company, and webhosting with another one. So, if you someone who can share their webspace with you, you can simply register a domain name from any registrar, and start hosting 
Some technical stuff
What makes a website ? ( from a webhost’s view ). It’s a domain name and some server space. It is possible that, domain name is registered at the company “A” and the server space is at company “B”.
