The recent question "Has anyone ever named a war after their own country or faction?" led me to mention that The War of the Grand Alliance (also known as "The War of the League of Augsburg" or "The Nine Years' War") might be a possibility. However, after some quick searching, I didn't see anything that said definitively whether anyone within the Grand Alliance / League of Augsburg actually used the name "War of the Grand Alliance" or "War of the League of Augsburg" or not.
For reference as to which countries / areas would count as having used the name, the Wiki article on the Grand Alliance says the following regarding its membership:
The Grand Alliance was a European coalition, consisting (at various times) of Austria, Bavaria, Brandenburg, the Dutch Republic, England, the Holy Roman Empire, Ireland, the Palatinate of the Rhine, Portugal, Savoy, Saxony, Scotland, Spain and Sweden. The organization, which was founded in 1686 as the League of Augsburg, was known as the "Grand Alliance" after England and Scotland joined the League (in 1689).
So, my question is: Did anyone within the League of Augsburg / Grand Alliance refer to the war in question as "The War of the League of Augsburg" or "The War of the Grand Alliance" or were these names just used later?