Cauchi is a Maltese surname.
This surname likely originates from Publius Gabinius Secundus Cauchius. He was a general under Claudius who upon defeating a German tribe called 'Cauchi' was given the right to add it to his name.
In the book of Acts in New Testament Apostle Paul is shipwrecked on Malta, where he meets with the Roman prefect whose name is Publius. It is highly likely that this Publius is the one and the same man, since the surname had to arrive in Malta somehow, and with him being honored with a significant trophy surname, it would be unlikely anyone else had it but him.
Furthermore in Maltese families they use family nicknames, which are sometimes more important to identity a family as they can be more unique than many shared surnames, and used to identify a family more specifically. There is a known family nickname 'Gabi' which belongs to a family surnamed Cauchi, which strongly leans towards a shortened form of Gabinius a Roman family name, and further supports the argument of the Cauchi Surname originating from this man.
If this argument is accepted, than it would make this surname attested and documented as far back as Suetonius 70AD making it one of the oldest documented surnames.
Notable people with the surname include: