Does anyone know the etymology behind the names of Celtic places and languages?

I was trying to find anything online about a specific question I have about celts/celtic languages and what not. Is it just a coincidence that Galicia, Gaul, Galatia (celtic Turkey) and Gaeilge are all related to the Celts, and all have the "gal/ gael/gaul" theme running through them? My first guess was that they're all similar in name because the words all originate for the general term Romans used for all Celts, but I couldn't find any evidence to suggest that. Thanks guys