Well, not necessarily "our" guys but our cousins and the cousins of all the other Celts.
The Celts invaded lands extending from Turkey to Spain and from Italy to the British Isles.
Extent of the Ancient Celtic World
"Galicia" derives from the Roman name meaning "Land of the Celts". So, you will find a "Galatia" in Roman Turkey and a Galicia in Spain. You will also find a "Galicia" in Poland corresponding to the easternmost extension of the Celts. The Roman name for Celtic France was "Gallia" and, as Julius Caesar has taught every schoolboy suffering through Latin class, "Gallia est omnis divisa in partes tres..."
The "Dying Gaul" is a famous statue from the ancient Greek city state of Pergamon in what is now Turkey commemorating a victory over the Celts in 239 B.C. The battle dress (buck naked), the battle trumpet, the shield and the gold neck collar (torque) is typical of Celtic warriors and is identical to the battle gear encountered by the Romans in their wars with the Celts in northern Italy, France and northern Spain.
The Celts did succeed in conquering central Turkey and that became the "Galatia" of St. Paul's letter.
In the British Isles, the Romans pushed back the Celts into Scotland and Ireland which was never invaded by the Romans. The Germanic invasions of Britain by the Angles and Saxons replaced the Romans in England but the Celts kept their bastions in Scotland and Ireland. The Romans could have called Britain "Galicia" also. Instead, they named it "Brittania" which was a corruption of the Greek name "Pretanic Islands" which in turn came from "Pritani" which is what the Celts in Britain called themselves.