Cool. I have this ancestry as well. Of course, it's more common in Canada :/ Apparently, if I can prove my lineage, I am eligible to add "UE" to my name.
Being a descendant of the Loyalists is the genealogical equivalent to being a Mayflower descendant for Americans. I believe I also have a Mayflower ancestor, so I've got both. (The Washburns have been in North America since the 1600s, and were at one point a powerful political family in Massachusetts; one of the branches leads to a Mayflower passenger)