Every one of Kakashi's ninja dogs has a symbol on its back that looks like a face:
What is this symbol and what is its meaning?
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It's a pretty interesting explanation... In this wiki for Ninken (Ninja dogs):
They all have a face-shaped design on their backs called Henohenomoheji (へのへのもへじ) — which is the sound made when all the characters in the face are put together. Appropriately enough, children use this design as the face for their scarecrows, which is "kakashi" in Japanese.
Basically, if you consider the picture you included:
So, へのへのもへじ (henohenomoheji). The first "heno" is repeated because you have a pair of eyes and eyebrows.