Add Contact Suffix to Quicksearch Results
At Administer - Customize - Display Preferences, near the bottom there is "Individual Sort Name Format". If you change it to {contact.last_name}{, contact.individual_suffix}{, }{contact.first_name} then NEW and UPDATED contacts will start to appear in quicksearch as desired. The only thing is that existing contacts who haven't been re-saved will still appear the old way. If you only have a few then just go edit and re-save them.