Hachiken found this stray dog while doing the second field cleanup after joining Ooezo Agricultural High School.

Since it was a stray dog, he didn't have a name. After some help from other clubs who made the dog's house they named it Vice President's dog or Fukubuchou in Japanese (Hachiken was the Vice President of the Equestrian Club at that time).

Later in the series and manga, we can appreciate the small bamboo collar with the "Pocket Money" tag, the dog pays its own expenses (Vet or food) with that. Hachiken tamed it too.