When you first start blogging, you may begin with a free blog platform like Blogger but as you become serious with blogging, you may want to move your blog to a good host and get a good domain name (which I highly recommend).
Once you decide to buy a domain name you will need to find one that is not registered yet, which is not easy as most of the domains you can think of may have already been taken.
To save time you can use these services:
* Namebay – ICANN accredited registrar for your domain registration and availability check
* Instant Domain Search – checks the availability of a .com, .net and .org domain as you type
* AJAXWhois – checks the availability of a domain for your preferred extensions as you type
* Domjax – free domain name search tool
* DomainsBot – suggests available domains
* Dyyo – helps you find 4 letter domain names
* 5Letter – helps you find 5 letter domain names
* Whois Source – lets you know if a domain is already registered and displays the details of the registration
Choosing a domain name
I personally prefer choosing domain names that are short, easy to remember and with keywords in it that describes what the site is about. But there are sites with domain names that give you no idea what the site is about and yet are very popular (like Orkut, YouTube,Pownce,etc).
I don’t recommend domains with hyphens and numbers in it (my mistake with Blogg-Buzz) as they make it hard to remember and to tell someone about it.
Also try to always choose a .com domain as that is the most popular and people will mostly assume your domain name to be yourblogname.com, even though it may actually be yourblogname.net and as a result you will lose visitors.
If you plan to start a personal blog, a domain name with your name in it would be the best option but be careful if you have long names. Like for example my name is not really JohnTP, its John T Puthenmadhom and if I had chosen www.johntputhenmadhom.com for this blog I would never have had as many repeat visitors as I currently get as visitors would find it hard to spell my name. So instead I chose www.johntp.com which is a shorter and easy to remember domain name.
Source JohnTP.com