Gaelic names were used by the Celtic inhabitants of Ireland. Some Gaels (the Scots) migrated to northern Britain from Ireland in the 5th century. Gaelic names usually consisted of a given name and a byname.
Given names were chosen from a traditional pool of names, derived from Gaelic. Over time, the given names used in Ireland and Scotland diverged somewhat. Around the 5th century the Gaels (first the Irish, then the Scots in the next century) became Christianized, and thus Christian names began to be used alongside traditional Gaelic names.
Brythonic names were used by the Celtic inhabitants of Britain (called Britons). In the 4th century Britons from England also began migrating to Brittany in France. Brythonic names normally consisted of a given name and a patronym. Given names were originally derived from Brythonic but after the Britons became Christianized some Christian names came into use as well.
Celts inhabited much of Europe in ancient times, not just Britain. In France and Belgium there were Gauls, in Spain and Portugal there were Celtiberians, in Switzerland there were Helvetii, and in Turkey there Galatians. Celts also inhabited Germany, Poland, Hungary and northern Italy. Unfortunately there are very few records of the names they used.