Clicking the Add DN link creates a custom phone button template for that phone. If you do a lot of phones like this, it will become a bit messy. Instead under the Device menu, then Device Settings, select Phone Button Template. Find the one for a Standard 7961 and copy it (don't modify the current one as this will change all current phones with that template specified). Once you name it, you can specify which each of the buttons do (DN, speed dial, service..).
Now on the phone you need to update, assign it the new phone button template and click Save. It will then show the appropriate number of DNs on the left side to be configured.