We is Welsh?

In the 9th Century three indigenous tribal groups shared what is now Scotland (with the Angles from Germany who ruled what we call Lothian and the Borders). 
The three indigenous kingdoms were Dalriada (Gaelic speakers from Ireland), The Picts and the Kingdom of Strathclyde. Strathclyde stretched from the Clyde in Glasgow, through Dumfries and Galloway and into Cumbria, it was peopled by the North Britons who spoke a form of Welsh and were part of the same tribal group who once occupied most of the British Isles but were now confined to Wales and Strathclyde after the invasion of Southern Britain by the Saxons, Angles and Jutes from mainland Europe.

Eventually things resolved themselves with the English claiming an Anglo-Saxon (German) heritage while the original folk of Britain became Welsh, Scottish and Irish. Gaelic won the language battle in Scotland (though Welsh could still be heard in Scotland in the 12th Century and 'Scots' is derived from Old English (German)). Penpont is just one example of a Brythonic (Welsh) name in D+G.The name Cumbria is derived from Cumbric (the form of Welsh spoken there) - people seem to have called themselves Cumbri the same way that the Welsh call themselves Cymry (most likely from British *kom-brogi meaning 'fellow countrymen').

Tim Clarkson has written the definitive history of the Gwyr y Gogledd (Men of the North) - The Britons of Southern Scotland - here and has a blog about Govan the royal capital of StrathClyde from 800 - 1050.