Blogging – custom domain
If you are a current blogger on Blogspot and you register a custom domain the word ‘blogspot’ will automatically be removed from the blogspot.com URL address giving your blog/web pages a more personalized and professional appeal.
As a background information, Blogger is only a free publishing platform, and you need a domain to work with it. To provide free blogging experience, Blogger uses Blogspot as the free domain. So when you sign up with Blogger, you can get a free domain like http://www.example.blogspot.com.
Now, if you want to remove the .blogspot.com from your address, here are some methods to do it :
Use your own domain, move your current blog to your own domain. For this, you can get a more professional web address like http://www.yourname.com. However, if you choose this method, you need to pay some money for such address.
If you want a free domain (but not blogspot), you can use www.biz.ly and others. They will provide you with a free domain (or domains). Then you can move your blog to this free address.
However, there are some drawbacks of doing this. Blogger (Blogspot) provide their users unlimited traffic and storage, and the domains above do not. Each of them will have some specific bandwidth and storage limits for you to deal with. In addition, you have to pay some money for them.
this is from bloggerfanatix