Yes indeed, a simple algorithm that adds a subsequent number after the user's name + device type.

User's Name/ID + Subsequent Number + Device Type = Kas's 3rd Kindle

When I registered my new iPad Pro 9.7 with a Kindle app a couple of months ago, it knew I already had registered an iPad Mini 2, so it called the Pro:

User's Name/ID + Subsequent Number + Device Type = Jack's 2nd iPad