I found a great thought on one of my favorite websites Useit.com the other day, and a powerful argument for having your own name for your blog.
Jacob Nielsen says:
Having a weblog address ending in blogspot.com, typepad.com, etc. will soon be the equivalent of having an @aol.com email address or a Geocities website: the mark of a naïve beginner who shouldn't be taken too seriously.
Letting somebody else own your name means that they own your destiny on the Internet. They can degrade the service quality as much as they want. They can increase the price as much as they want. They can add atop your content as many pop-ups, blinking banners, or other user-repelling advertising techniques as they want. They can promote your competitor's offers on your pages. Yes, you can walk, but at the cost of your loyal readers, links you've attracted from other sites, and your search engine ranking.
Sure, Wordpress and the ilk are free, but you can have your own domain name for just a few bucks more - I've seen for less than $10 per year. Make the investment up front, and own your blog yourself.