In this series, the rabbit samurai character is given the name Usagi Yojimbo. In the comics that is the title of the comic, the character is named Miyamoto Usagi.
It's noted in the episode "Usagi Yojimbo" that in Japanese the name translates to "Rabbit Bodyguard".
After Usagi Yojimbo destroyed the Foot Soldiers and Michelangelo was ready to fight them, Donatello says to him "uh forget it Mikey, our friend Usagi's taking care of everything". This is the only time in this series of the Turtles is addressed by their nickname just like in the comics, movies and later TV series'.