Correct. It is named the 'Adidas Originals X Coca Cola Climacool 1'. The shoe has a range of colourways, all of which feature the colours that are synonymous with the Coca Cola brand: red, black, white and silver.
There is no overt Coca Cola branding on the shoe, and unless a person knew the shoe was called the 'Adidas Originals X Coca Cola Climacool 1' they would be mistaken for assuming it was simple an Climacool shoe in black, silver and red. The Climacool was one of the first Adidas shoes to feature a full breathable mesh fabric upper.