Whilst we first see Gatt listed in 1420, older documents show a Francesco Gatto as castelan at Fort St. Angelo and a feudal tenant at Deyr il-Bniet in 1350. His descendent, Saveiro Gatto, would become a Baron in 1783.
Almost certainly from the Italian gatto, meaning "cat", perhaps given to a person who displayed feline characteristics. It could also be a corruption of the Italo-Greek name Agata, from the Greek agathos meaning "good, honourable”.
In heraldry, a cat signifies freedom, vigilance and courage.