Gleann Laoigh Beag
Gleann Laoigh Beag is a glen in the upland of Mar that runs from the confluence of the Laoigh Beag with Uisge an Doire (where they combine to become the Laoigh) up into Coire Sput Dearga. The name ‘Laoigh Beag’ is shared by the burn, glen, cottage, and locality around the cottage near the mouth of the glen.
As a place name Laoigh Beag means little calf-one, a reference to the river - it's the 'little calf-one'. The glen takes its name from the river ; it is Gleann Laoigh Beag meaning glen of little calf-one.
There's no doubt that Luibeg Cottage gets its name from the river, by way of the glen. However - I'm not comfortable with retrospectively applying pure Gaelic names to 19th century buildings without evidence that the pure Gaelic name was actually used. So, for now, I'll leave Luibeg Cottage as it is.
Laoigh Beag is a good example of how a Gaelic place name can be half-mangled over time, and left stranded somewhere between Gaelic, Scots, and English.
On the old 6-inch map (1869) the place name is shown in the form Glen Luibeg, and I've not seen any Ordnance Survey map that show it in any other form ; that's odd for two reasons.
First - it's shown on earlier maps, Robertson (1822) for example, in the more correct Lui Beg form. Second - it's correct Gaelic form seems so apparent that it's surprising that the Ordnance Survey didn't collect its correct Gaelic form in the 1866 survey, while they correctly collected the Gaelic form of Coire Odhar, an arguably more problematic place name.