Purchases made via an admin shop where the name has been changed from "Admin Shop" in ChestShop are not ignored.

Doesn't look possible as far as I can tell. Please provide the command you ran to access that, your plugin config as well as your chestshop config.

CSN config hasn't been modified.
Command used: /csn history Server Shop
ChestShop config (irrelevant entries omitted):

# First line of your Admin Shop's sign should look like this:
ADMIN_SHOP_NAME: "Server Shop"

CSN config hasn't been modified.

I mean if you don't disable the logging of the admin shop in the CSN config then how do you expect it to get ignored?

I was under the assumption it wouldn't write entries for the admin shop into the database as that would be unnecessary?

Well historically it used to track all shops until the config option was added (which defaults to tracking to not break existing setups). Some just want to see how their admin shop is used I guess, for the rest the config option exists.