is not quite correct. The AKC does not assign a number to the first one.
Open the Dog Name Check [1]. Pick a breed, enter a unique dog name, and the page will report it is available. Now pick a semi-unique combination ("Shih Tzu" + "King") and the page will say "The name chosen has been used previously, but may be used with the following change: King XXXVII." This implies the first person to pick "King" got "King" and the second person got "King II."
One dog per breed can have the name Spot/King/etc. But the AKC is a rent-seeking monopoly and 6 Roman numerals is short enough to still appear somewhat exclusive.
Open the Dog Name Check [1]. Pick a breed, enter a unique dog name, and the page will report it is available. Now pick a semi-unique combination ("Shih Tzu" + "King") and the page will say "The name chosen has been used previously, but may be used with the following change: King XXXVII." This implies the first person to pick "King" got "King" and the second person got "King II."
One dog per breed can have the name Spot/King/etc. But the AKC is a rent-seeking monopoly and 6 Roman numerals is short enough to still appear somewhat exclusive.
[1] https://www.apps.akc.org/apps/reg/namecheck/index.cfm