Especially Welsh names. Welsh names are all Thomas, Jones, Williams, Hughes, Lewis, Davis, etc. Scottish bit more easier to trace. Irish difficult to trace because so many Irish about the place, especially in migration records.
Celtic is such a broad designator though. The French can be considered Celtic and perhaps the people who are now English were once Brythonic (Celtic).
But there are some who say that when the Anglos and Saxons (and Jutes) came over they genocided all the native Brythonic Celts and pushed beyond the mountains of Wales. They say that the modern Englishman has more DNA in common with Northern Germans than they do with the Welsh.
But DNA studies conflict. And it’s always troublesome reconciling ethnicity/nationality with DNA.
Scotland for example is a difficult case. Today we see one ethnicity called ‘Scottish’. But originally Scotland was inhabited by the Picts who were probably Celts.
And then the Irish invaded from the West and into the Highlands, these became known as the Scots. And the Anglo-Saxons held the land of Northumbria which includes Southern/Lowland Scotland.
Eventually the Irish Scottish Kingdom absorbed the Pictish Kingdom erasing Pictish language and culture within a few decades. Then the Scottish Kingdom took over both the Anglo-Saxon Kingdom in Lowland Scotland and the Brythonic Kingdom of Strathclyde next to that.
Hence Scotland is really a story of Irish Gaelic Warlords coming over in boats and taking over land from three other peoples: Picts, Anglo-Saxons, Brythonic.
But the Anglo-Saxon community under Scottish (Irish) rule continued to use their own language, a form of Old English now called ‘Scots’. And this Scots speaking community expanded and resisted Gaelic domination, and spread throughout Scotland.
Most ethnographers define ethnicity by the language one speaks and identifies with. Most people who have been Scottish in history were Scots speakers* not Gaelic speakers. I.e. they were a Germanic speaking people.
So my point, that Scotland shouldn’t be so readily identified with Celtic.
Also generally, most of the Germanic speaking Scots are the Protestants, while Gaelic heritage Catholic.
*Primarily post the middle ages and before the 19th century when received pronunciation and standard English English became the norm.