Max is a name that means “the greatest.” Variations includ Maximus and Maxwell. Breeds most often named Max include Yorkshire Terriers, Boxers, Bulldogs, Golden and Labrador Retrievers and German Shepherds. It is a strong name that indicates intelligence and bravery. Owners who think that their dog is the greatest are most likely to name their dog Max. When you think about the name Max, it suggests the most or the best because we use the abbreviated term of maximum as max to describe something that has reached its full potential. Then there are dog owners who just like the name Max because it is short and easy for a puppy to learn. There are several reasons why people in the United States name their dogs max.