Didn't Scotland have many migratory waves? At least I'm pretty sure I probably have little genetic information in common with the North-Western Germans from 3000 years ago.
We have had many, many migratory waves, but I do have a rough idea of who my ancestors were. My father took a DNA test as part of a Scotland-wide research project with the intention of understanding the genetic makeup of modern Scots. The test would identify the various genetic markers that people carry that tie their paternal/maternal ancestors to a particular place in time, and through that method we can learn that people may have markers that identify their paternal (father's father's father etc) ancestors as ancient Scots, Picts, Berbers, Vikings, Anglo-Saxons and so forth. The markers that have been passed down to me indicate that our ancestors belonged to the original Celtic inhabitants of the Isles who primarily came over about 7000 years ago, displacing the original hunter gatherers.
Exactly which Celtic nation my ancestors belonged to however is very uncertain. Our marker has not been identified yet in the study, but I know that we are not Ancient Irish, we are not Pictish, we are not Vikings. We may either be Strathclyde Britons, Britons/Celts from elsewhere in the UK or another grouping altogether. I don't know how our genetic history compares with the ancient Scots (the original Scots), I don't think our marker was identified as Scottish though. They told us that if we belong to an unidentified marker "we are probably Pictish", that has been disproven. If I remember correctly we have the most in common with Scottish people as a whole and Northern Irish as a whole. That is to be expected of course, but that may mean my ancestors were a part of the various Celtic kingdoms in the North of Ireland and West Coast of Scotland. Who knows.
My theory is that we are Britons of some description from the mainland given that our biological paternal ancestors took a Scots/English surname based on a profession, as so many Britons and Welsh people did when they were forced to take on a surname to facilitate taxation. As far as we know, our paternal ancestors lived in Strathclyde and the surrounding region. We are Celts of some kind, that has been confirmed, but it's probably been a very long time since we were native Celtic language speakers. I know the very idea of "Celtic peoples" is quite sketchy in that the Celts exist as a linguistic group, not necessarily a genetic group, but my genetic markers are part of the same group as Picts, Scots, Irish and Britons. The same group that entered these islands 7000 years ago. It's perhaps notable that I am part of a relatively unbroken chain of fathers and sons who have lived in the British Isles for 7 millennia.