The translation to Scots Gaelic for "great sword" is "claidheamh mòr".
"Two-handed sword" is "claíomh dhá-láimh".
"Basket-hilt sword" is "claidheamh basgaid-fèileadh".

So, I suppose it would depend on how one describes the two-handed sword: as 'two-handed' or 'great'. Personally, I don't think I would call a basket-hilt a great sword, though. Just my opinion.

I have also read somewhere - the source escapes me at the moment - that there were two-handed swords cut down and re-hilted to the smaller-sized basket-hilt swords to be used in regimental service and the name 'claymore' stayed with the cut-down sword.

That may have been purely speculation.