GooDooper, Goodyooper?
That’s going to be a sub-brand, marketed only in the Upper Peninsula of Michigan.
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I think your headline needs to say… Goodyear bought Cooper 
Sort of like the “merger of equals”, Daimler and Chrysler! 
Goodcoop? Or in homage to the past year of isolation for so many, perhaps CoopYear? 
I don’t know about Cooper. I have Goodyear Weather Ready. Drove 100 miles yesterday in slick slush with little problem. I suspect they’ll keep their trade names and separate plants without reading the article.
That is what the plan appears to be.
“Gooper,” perhaps?