The Latin history of the names goes obviously back to the Roman period when the Roman legions marched across Europe around 56 BC. They swept into the islands along with Gaul and made them outposts for trading. Jersey was given the name “Caesarea”, Guernsey “Sarnia”, Alderney “Riduna”, Sark “Sarnica” and the smaller islands being Herm and Jethou, Armia and Sarmia.
When the Bretons arrived around 525 AD Guernsey was given a new name called “Lesia” with Jersey becoming “Angia”. However, the greatest influence was the Vikings who bought with them a new Norse language, which developed along with the islands’ new names with the “ey” at the end of the names literally translating to “island” in Norse. Of course there are variations to Guernsey/ Jersey French but the identity still remained Norse to the present Jersey, Guernsey and Alderney.
So the name “Aurigny” from what I make of it, is just a French word with the English being Aurigny derived from Norse. If you look at some of the French town names you will see some other examples. And so from there you get Aurigny Air Services.