The phrase "tag number" refers to a specific identification number assigned to an object or person, usually to distinguish it from others. It helps to keep track of the item or individual, making it easier to find or identify them. Full definition
If your pet is lost, the finder or the animal shelter can trace you through the rabies tag number at your veterinarian's office. (bestfriendsofpets.org)
Your dog will be given a permanent license tag number. (burbankpd.org)
Use your cell phone number as a dog tag number. (platpets.com)