Does anyone know the Old Town Alexandria VA law for boarding in your home with Rover?

There are going to be two different issues: (1) Are you a kennel and does it need to be licensed as a business? (2) Does your municipality's zoning laws allow you to provide boarding where you live?

Fairfax County defines a kennel as "An establishment primarily engaged in boarding, keeping, training, breeding, or handling dogs, cats, birds, or other small domestic animals for a fee." The key word there is primarily.

PET SITTING Up to four companion animals not owned by the resident are also permitted to be sheltered, fed, and watered for a fee in a dwelling; if caring for dogs, the total number (including those owned by the resident) must meet the dog unit limitations in the table above. This standard allows for accessory pet sitting services such as Rover, DogVacay, and Fetch, without the need for a special exception. A resident may submit a special permit application to the Board of Zoning Appeals (BZA) to request an increase in the number of dogs permitted on a lot under the dog unit limitations above for dogs owned by the resident, but the BZA may not approve more than four dogs not owned by the resident (as this would be considered a kennel or animal shelter).

https://www.fairfaxcounty.gov/planning-…

That link also has contact information.