The face can get dirty pretty quickly, but speaking of treating tear stains, I will answer this with “If you must”.
I personally prefer not to medicate the eye area for tear stains. If you have decided that looking at the reddish tint around the eyes is something you can’t tolerate, then my suggestion is a prescription from your veterinarian called Poly-Otic. This is a powder you dust over the pups food and it develops in the pups system to end the tear stains.
Dark colored pups have the same tears and you don’t see the stains. But on most all of the pups, the tear stains can be washed every day or every other day so bacteria doesn’t affect the eye area. There is a cleanser for the face of pups that is called SPA Facial Scrub, I get it thru PetEdge, an online catalog. I like it and it works so well that the time spent having to wash their faces can be once a week on most of my pups. It is like a retardant that cleanses the area but also works to arrest any foul odors caused by the bacteria.