There are a couple of sources, including Diana Henderson's The Scottish Regiments and the Osprey Men-at-Arms series which suggest the Royal Scots Greys took their name from their original uniforms, which were grey. I've been unable to find an image of this uniform, and as we're talking 17th Century, it's unlikely one exists.

It's interesting how these origin stories get muddled and muddied in the mists of time.