Eddy's most likely started out as a parody of the real-life chain Ralph's and then was changed to be more of a Walgreens parody with ATS as it would be more recognizable.
Eddy's first appeared in the 18 Wheels of Steel series as a Food company. It had a different, much more plain logo, consisting of a yellow background and the name written in blue, white, and red.
The company logo could be inspired by the Swedish paper manufacturer Edet.