Besides the RHR, there were several other Scottish Regiments in Iraq:

The Argyll Sutherland Highlanders
The Highlanders (Seaforths, Gordons and Camerons)
The Royal Scots Dragoon Guards
The Royal Scots
The King's Own Scottish Borderers
The Royal Highland Fusiliers
The 51st Highland Volunteers (Territorials)

Cheers,

Todd