The name is a play on the Rhodes Scholarship, and is formed from Cody's last name and Damien Sandow's claim to be a teacher of the masses (like an educated scholar).
They announced their name in response to the formation of Team Hell No, so the addition of 'Team' as a prefix to their title is based on that. WWE.com has abbreviated this to The Rhodes Scholars in an article.
Cody was in the middle of a feud with Sin Cara, and Damien was in the middle of a feud with Brodus Clay. They initially united against these common foes.
↑Cody Rhodes & Damien Sandow attacked Team Hell No : "Cody Rhodes and Damien Sandow stormed the ring, stunning the Tag Team Champions and debuting a name of their own: "Team Rhodes Scholars." The Rhodes Scholars didn't stop there, however, seemingly laying down a challenge for Hell No's Tag Team Titles. It would appear that chair attack from SmackDown has not been forgotten."