UncleEbenezer wrote:What does [Alba] mean to a Scot? Is it a widely-used name? Part of the heritage you grow up with, that's all around you?
Alba is, as others have noted, the Gaelic name of Scotland. Most, if not all, people will be aware of the name, as it will have come up, amongst many others, in geography and history lessons at school as examples of placenames that have Gaelic, Norse, Pictish or other roots (and, unlike Alex Salmond, most of us will have been taught that it is pronounced more like al-a-ba (with the "b" somewhere more between "b" and "p")).
In more recent years, awareness of the name has increased, through the longstanding and fairly well known welcome in tourist leaflets "Fàilte gu Alba" (now also seen on road signs at border crossings), the creation of the Gaelic tv channel BBC Alba, and the increasing use of bilingual names for public bodies (although I expect most of them would panic were someone to actually try to communicate with them in Gaelic). I suspect that for most people, it's not very much more than that: part of the "background" heritage of the country, something that we are glad is now acknowledged and given some support, but mostly have no more than a casual interest in (eg, placenames).
Whether it has more meaning than that to individual people probably depends more on whether one is a (native) Gaelic speaker, or has Gaelic heritage, and, possibly not least, one's feelings and/or strength of feelings about independence.