Hi Tammy, the name of the bucket is Cuisinart Ice 30-RFB 2 Qt freezer bowl stainless steel. I have got to get one myself because you definitely need a second one. Glad to help and hope you find this information helpful.
its just called an Ice Bucket... You can go to the website www.cuisinart.com to order another as a backup. That is what I am about to do as well. We get so much use out of this too! I hope this helps. Have a Great Day!