I would still like to know what the beagle's name was. Assuming the canine life expectancy in the 22nd-23rd century is ~20 years, we have to think Jon was on his fifth or sixth, which would mean he ran out of Musketeers.
Maybe he started adding numbers. Porthos VI
With colons. Porthos VI: The Son of Rover.
Then, he rebooted the genetic line and called the first new puppy born in that line just, "Porthos." But, a lot of people said the dog looked nothing like the original to them.