Use a safe, soft ball (kush ball, plush ball). Facilitator tosses the ball to someone and that person says their name as he/she catches it. Then the person tosses it to a second person who says his/her name, and so on, until everyone has caught the ball and said their name. Then you go around again, only the person throwing the ball has to say the name of the person as they're throwing to them.
Keep doing that until everyone can throw the ball to anyone and say the name as they throw... There is another aspect of tossing the ball around that could also be considered. As in the 'going around the circle,' time how long it takes for everyone to touch the ball and say their name, and then tell them to improve their performance. That wording of the instructions is extremely important. They will probably come to the idea of getting close together, each touching the ball, and saying their name all at once.