Exactly correct. I worked in Sears Tower in one of the appliance buying departments and even though the appliances were manufactured by Whirlpool, Roper, Litton, they were branded as Sears Kenmore. Same with Craftsman tools and Die Hard batteries.
I wonder why some of the cart names were changed. “Circus Atari” to “Circus” is understandable due to the Tele-Games branding, and “Outlaw” to “Gunslinger” may have been due to Sears being concerned about not promoting “lawlessness” in a family oriented store (shooting the other guy seemed to have slipped through the cracks, but I digress), but “Star Ship” to “Outer Space”, or “Maze Craze” to “Maze Mania” isn’t as clear. They didn’t do it to all carts, just some, and I wonder what the logic was.