But technically it's just Scottish the language as it is referred to in English there's no need to add Gaelic at the end. Gaelic would be "Scottish language" in Scottish.
Just as Irish is a language and in the Irish language Irish is Gaeilge.
It's pretty confusing but I think I got it right! Koralatov could explain better below. I'm about 4th generation Irish folks left problem late 1800s from Co. Monaghan.
Slán!
GordonS is right: Gaidhlig is only ever referred to as "Scottish Gaelic" or, more commonly, just "Gaelic" by Scots on a day-to-day basis. The concept of "Scottish" as a language is pretty murky and is generally not used seriously. Even in these days of awakened Scottish national identity and independence referendums, we all still speak English of a Scottish variety and call it English.
Calling Gaeilge "Irish" and Irish English "English" makes a lot more sense, frankly.