· Medical Trivia Team Names. Following are the best medical trivia team names for your inspiration: Run So Far-ians; Sisters With Blisters; Sometimes A Great Notion; Straight Off The Couch; Trojan Track; Upright and Smiling; We Nose Everything; Fast Women; Venous Vikings; Fatal diseases; Say Ahhh; Purple People Eaters; Bedpans and Tube Sticks; The ….