Scots = first "Scoten" then later changed to the modern German word "Schotten"

as per this Encyclopedia Britannica reference:

"any members of an ancient Gaelic-speaking people of northern Ireland who settled in Scotland sometime in the 5th century AD. Originally (until the 10th century) "Scotia" denoted Ireland, and the inhabitants of Scotia were Scotti. The area of Argyll and Bute, where the migrant Scots settled, became known as the kingdom of Dalriada, the counterpart to Dalriada in Ireland. St. Columba inaugurated Christianity among them and helped raise Aidan to the kingship of Scottish Dalriada in 574. The Scots then expanded eastward into what came to be known as the Forest of Atholl and Strath Earn (valley of the River Earn) and northward into the area of Elgin. The union of the lands of modern Scotland began in 843, when Kenneth I MacAlpin, king of the Scots (Dalriada), became also king of the Picts and, within a few years, joined "Pict-land" to "Scot-land" to form the kingdom of Alba. By 1034, by inheritance and warfare, the Scots had secured hegemony over not only Alba but also Lothian, Cumbria, and Strathclyde--roughly the territory of modern mainland Scotland. In 1305 the kingdom was divided into Scotland, Lothian, and Galloway; in the 14th century Scotland came to be the name for the whole land, and all its inhabitants were called Scots, whatever their origin."

- Hope this helps - Dan