What is the name of the dog

Marie went to market with a horse and a dog to buy a kilo of tomatoes...
the name of the horse is busiphalaus...
she rode on the horse,
yet walked...
She came back home after an hour of shopping..

What is the name of the dog?...

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The name of the dog is YET.
It is given in the Puzzle "She rode on the horse, YET walked"