I used to sell appliances a while ago for Sears. In the past Whirlpool made most Kenmore products (washers, dryers, refers, freezers). That has changed. The way to know who makes a certain Kenmore product is to look at the first three numbers of the model #, which is then followed by a decimal and the remainder of the model #. It was and still is hard to beat Sears for customer service. I've seen them take an appliance back from a customer that was owned for years.
My last freezer I bought at Home Depot though. A Maytag, and not frost free. So far so good with it. I bought it about 8 years ago.
Kenmore refers/freezers are now made by Whirlpool, Amana, GE, Frigidaire to name a few. One thing I noticed a while back if I remember correctly was no matter what the brand, they all used the same compressors made by Embraco in Mexico.