That makes sense. I guess my question is: How does the Ashigaru server create the PayNym from the payment code? Does the server just randomly make a PayNym and assign it, or does it use the payment code and use some kind of hash to create it? And, how are the Ashigaru PayNyms compatible with Sparrow? Do they use the same server?

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They will be using the payment code (or hash of payment code) as the seed for an image+username generator.

As of a recent update Sparrow, they both point to the same webserver.

Great info. Is that image/username generator code available?

I don't believe that codd is available. It definitely wasn't for Samourai, since Ashigaru were unable to recreate the same Avatars and PayNyms used by Samourai. There might be some security concerns with opening up the exact algorithm.