Yes, you can keep the domain and redirect the name servers (see 4. below).
WordPress.com and WordPress.org are completely separate.
Here's a summary of the process involved.
1. Hire a web host http://wordpress.org/hosting/
2. Set up a WordPress.org install and equip it with a theme and plugins.
3. Export your content out of your WordPress.com blog http://en.support.wordpress.com/export/ and import it into the install.
4. Purchase a site redirect upgrade from wordpress.com
http://en.support.wordpress.com/site-redirect/ or if you have domain mapping then update the nameservers http://en.support.wordpress.com/domains/domain-management/
5. Transfer subscribers and stats. See http://en.support.wordpress.com/moving-a-blog/moving-your-subscribers/
6. Set your wordpress.com blog visibility to private. To change blog visibility to private go to > Settings > Reading scroll to Blog Visibility and choose option 3 . See the guide here http://en.support.wordpress.com/settings/privacy-settings/
Alternatively you can purchase a Guided Transfer and Staff will do the move and set up for you http://en.support.wordpress.com/guided-transfer/
NOTE: WordPress.com and WordPress.org have different log-ins and run different versions of themes with same names. If you don't have a username account at WordPress.ORG click http://wordpress.org/support/ and register one on the top right hand corner of the page that opens, so you can post to the support forums there and receive advice from WordPress.ORG bloggers.