Not a coffee mug, but Valvoline handed these out, along with some other promotional materials, when they rolled out NextGen, a retail oil you could buy that was made with recycled used motor oil.
I got mine when I was working at Auto Zone while in A&P school from around 2011-2013. I still use it every day - it’s my water cup at work.
I’m sure some here remember it. There were also Maxlife and High Mileage varieties.
I don’t think it ever sold very well.
Somebody here might remember when it was discontinued.