If your host will allow it, you can install Wordpress to run on your own domain. This may be preferable to using Wordpress.com for branding purposes. In addition to keeping the domain name of your blog totally under your control, by installing on your own server you have more freedom in how you configure the software, what theme you use (including one that's totally custom for you, or that matches your main website) and what plugins you install.
You can download the software at www.wordpress.org
. There is also extensive documentation and a support forum. You do need to have a bit of technical savvy (or a web hosting company that will support you in getting set up), as well as a host that supports PHP and MySQL, but on the whole I found installation and setup pretty straightforward.