This question is a bit difficult to answer, because—even if all your ancestors lived in lowland Scotland since the deep prehistoric past, and they almost certainly didn't—the names you list aren't terms your ancestors would be likely to recognize. ... But there's hope in archaeology!

Variations of the word 'Celt' do date back into classical antiquity. It originally referred to a specific tribe in southern France, although Caesar claimed that people throughout the region of Gaul (roughly modern France—so any ancestors from lowland Scotland were certainly not Gauls) were calling themselves Celts by 50 BC. Much more recently, antiquarians expanded the meaning of 'Celtic' to include any Iron Age society that looked similar to Caesar's Celts, or any culture that spoke a language that could reasonably be related to Caesar's Celts. But since Roman culture and the Latin language overwhelmed many of the areas that could fall into this category, modern uses of the word 'Celtic' often refer more narrowly to the cultures around the Irish Sea, or even more narrowly to Ireland exclusively. But the terms used by modern linguists, Roman generals, and Greek geographers probably have very little to do with what Iron Age peoples in lowland Scotland actually thought about themselves.

Picts are probably your best possibility, although here too there's possible reason for doubt. The Romans were very smart about how they managed their borders, but they didn't always understand how their neighboring societies were organized ... and Roman authors often had little interest in describing these societies accurately. (Tacticus's Germania is perhaps the best example of Roman ethnography that should never be read at face value.) So even though Romans dealt with Picts, and although some of these people probably described themselves as Picts at least to make things easier when dealing their powerful neighbors, it's not at all clear how important 'being Pictish' would have been for someone living in lowland Scotland.

Anglo-Saxon is, perhaps unsurprisingly, another troubled word. We know now that much of early Anglo-Saxon history (i.e. tribes coming from across the sea) was probably made up or at least greatly exaggerated, although this myth-making first appears during the Anglo-Saxon period itself. But the idea of an Anglo-Saxon community didn't really move from theory into practice until the very end of the Anglo-Saxon period, so this too is more of a historians' term than an idea that someone in the early middle ages would have understood. I've dealt with this problem a bit more here. But it's also important to note that 'Anglo-Saxon' is usually used to refer to peoples and kingdoms no further north than the borders of Northumbria, which doesn't quite reach into the areas of lowland Scotland.

Okay, so that's a bunch of no's and probably not's, which I know can be pretty dissatisfying. But I think it's really important to note that the ways in which we think about and describe the past often have little to do with how people in the past understood themselves, and if we lose sight of that, things like nationalism and ethnocentrism can spin wildly out of control terrifyingly quick. If you doubt me, I'd point you to a thorough work debunking the twisted legacy of Tacitus's Germania, or the broader survey about The Myth of Nations. The early middle ages can be a dangerous time, when placed in the hands of modern demagogues and hate groups.

More positively, we can say that at least some of your ancestors migrated to Britain back when the English Channel was just an extension of the Thames river valley. (The prehistoric land bridge has the earned memorable name of Doggerland.) There was probably a lot of internal migration within the British Isles, with a slow but steady back-and-forth with the Continent as well. The result? Well, one recent study has concluded: 'almost all European individuals, even when separated by large geographic distances (> 2 km), shared hundreds of ancestors within the last 3,000 years.' (Geary article, linked below, p. 69)

That brings us to the Bronze Age, when we can call people across the British Isles and much of northern Europe 'Celts', although keeping in mind that they saw a lot more diversity than Mediterranean-based authors or even their own archaeological record preserves. In the later Roman Iron-Age, it's probably appropriate to call them 'Picts', which has a bit more geographic precision and even seems to have functioned as a political community. For lack of a better term, scholars call the peoples living north of the Anglo-Saxon cultural area 'Picts' even into the post-Roman early middle ages, but it's important to remember that there was probably a lot of cross-pollination and hybridity between the two regions, and we know very, very little about how the people then living in Scotland would have understood themselves. Anglo-Saxon authors do, in fact, use the word 'Scots' during this period, but they almost always seem to be referring specifically to the peoples of Ireland.

During the Viking Age, the people of the Scottish lowlands found themselves living at a pit-stop for Norse traffic moving between the North and Irish Seas, which resulted in a heavy Scandinavian cultural influence. This certainly included some settlement, but I suspect there was more cultural colonialism than actual Scandinavian migration. By the later middle ages, 'Scot' had shifted meaning from the peoples of Ireland to the peoples of modern-day Scotland, although I must admit, there's a lot more history here than I'm personally prepared to discuss.

But keep in mind that this quick sketch only represents some of your likely ancestors. Scholars are increasingly sensitive to just how mobile past populations were, and as historians and archaeologists get better integrated into DNA-type studies, a lot of false assumptions are falling away. Many of the early DNA studies were really bad, and I'd pretty much given up interest in them until just recently (although other studies, like Strontium and Oxygen isotope analysis, have been quite effective). Now I'm pretty excited about DNA research, thanks to a new research project involving Pat Geary. With a few more years of hard work and decent funding, we might be able to say a lot more about how Europeans were migrating before modern shipping records evolved to give us a shot at tracking individuals. And as we focus more on the variations within the archaeological record rather than using over-simplified, anachronistic terms like 'Celtic', we'll be able to speak more confidently about who these people were and how they lived their lives.

EDIT: Thanks for the gold! Also a slight change of tone regarding Anglo-Saxon migration—this did certainly occur, but it's been much exaggerated. This has unfortunately caused us to ignore other migration events and background migration as well, which I wanted to give the front-seat in my comments above.