The word starts with a capital letter indicating it is a name (most likely a pet). A proper noun is the name of a person, place, or thing. If Spot is the name of something, then it is a proper noun.
A noun starting with a capital letter is not always a guarantee that it is a proper noun, people do get it wrong, so you must know the context of the noun's use. For example:
The new puppy, Spot left a spot on the carpet.