Is there a word or phrase for the following ice breaker game? A group of people form a circle, and the first person says their name. The next person on the left goes and says the first person's name and then their name. Third person repeats the process, and so on, until it comes full circle, and the last person has to recall everybody's name.
They are called "Name Games." For instance:
"Picnic: (An elementary school classic; it’s best to acknowledge at the beginning that it’s a little hokey.) Tell students you are going on an imaginary picnic. Ask the students to go around the room introducing themselves by saying their names and a food to bring that begins with the first letter of the name. (I’m Greg and I’m bringing grapes.) The next person must give the names and foods of everyone who came before, then his/her own name (That’s Greg and he’s bringing grapes; I’m Alice and I’m bringing applesauce.) Instructors usually go last, so that they have to repeat everyone’s name."