You can either add the code that follows to your themes functions.php or you can add the it to a plug-in. Just change the returns from the function to match your feed URIs and titles. There are two feeds the primary, which by default is the “Development Blog”, is limited to about 3 entries and the Secondary feed is much more open.

If you’d like to delete the feeds the just set the return to “”, doing this helps dashboard load time a lot.

/*
Plugin Name: Dashboard RSS replacement.
Plugin URI: http://www.completelypointless.co.uk/
Description: Changes the dashboard RSS to something more interesting.
Author: James R Whitehead
Version: 1.0
*/
function change_dashboard_primary_title () {
  return "Completely Pointless";
}
function change_dashboard_primary_feed() {
  return "http://completelypointless.co.uk/feed/";
}
function change_dashboard_secondary_title () {
  return "BBC News";
}
function change_dashboard_secondary_feed() {
  return "http://newsrss.bbc.co.uk/rss/newsonline_uk_edition/front_page/rss.xml";
}
add_filter("dashboard_primary_feed","change_dashboard_primary_feed");
add_filter("dashboard_primary_title","change_dashboard_primary_title");
add_filter("dashboard_secondary_feed","change_dashboard_secondary_feed");
add_filter("dashboard_secondary_title","change_dashboard_secondary_title");

That’s it, nothing too onerous or perplexing. I will say however that if you’re distributing themes or plug-ins that it would be nice to let wordpress keep their feed in there.