I'm not sure which specific 'a dog named Gucci story' you're referring to. There could be many stories about a dog named Gucci. It might be a story about Gucci's adventures in the neighborhood, like how it befriends other animals or discovers new places.
The story of a dog named Gucci could start with Gucci being a stray dog. One day, a kind-hearted person found Gucci on the street, looking all forlorn and hungry. The person decided to take Gucci in. Gucci then slowly started to trust this new human. As time passed, Gucci became an important part of the family. It would go on walks with the family, play with the kids in the yard, and guard the house at night. Gucci's presence brought so much warmth and love to the household, and it was always there to greet everyone with a wagging tail when they came home.