Countries of Europe Map, Learning & Quiz Game
This site--Seterra-- is free and you don't need to create an account (let me know if I'm wrong about this). This map automatically starts off in "Quiz" mode. To get the names displayed so you can learn them before playing, click on "Learn" on the lower right side of the map, and click on "Show all names" on the lower left side of the map.
After learning it, you can go to the lower right again and click on "Play." (The "Play" and "Learn" button is the same button--if you're already in "Learn" mode, the button says "Play" so you can switch to "Play" mode, and vice versa.