Not if it's only affecting Scotland... If it might get windy in Englandshire, then a named storm is likely 
FWIW I'm still hopeful of the Russian/Scandi high making an appearance. Hints have been modeled in FI and if we continue see lower heights in to Europe I believe this is a possibility.
Technically speaking though, a weather system will be classed as a named storm if there is at least an amber warning issued for that by the Met Office in the UK, or at least an orange warning issued for that in the Irish Republic issued by Met Eirann with that name being officially designated by whichever of those two bodies was the first to give out such warnings.
If the Met Office are doing their job properly, they are supposed to cover the whole of the UK and not just England. This means that if they are the ones who issue those warnings (and thus give such a system its name), this should therefore by rights, result in that system then being classed as a named storm even if these warnings only affect a small part of Scotland and nowhere else in the UK due to the fact that Scotland is itself, part of the UK and therefore, part of the area which is covered by the UK Met Office.
That is why if there is a forecast of possible storm force northerlies in parts of Scotland towards the end of this week from this particular weather system which could therefore potentially result in an amber warning there, that has to then lead to the possibility of that system then being officially named as Storm Caroline which is the next name on that list after all.
The north of Edinburgh, usually always missing out on snow events which occur not just within the rest of Scotland or the UK, but also within the rest of Edinburgh.