What is the participle or participial phrase in this sentence Spats name of my very spoiled cat.?

There isn't a participle or participial phrase in the sentence "Spats is the name of my very spoiled cat."

Let's break down why:

* Participles are verb forms that act as adjectives. They usually end in "-ing" (present participle) or "-ed" (past participle). Examples: "running," "played."

* Participial phrases are groups of words that include a participle and its modifiers. They act as adjectives, too. Example: "running down the street."

In your sentence, "spoiled" is an adjective describing the cat. It's not a verb form, so it's not a participle.