There's a very old tradition in UK of naming newly-raised regiments after various members of the royal family, not just after the ruling monarch.
I would also like to object to your characterization of the Loyalists as "backstabbing Quislings."
While some of them no doubt were, others were conservative and honorable men who held to their loyalty to King when others abandoned him, at the cost, in many cases, of all their property and even of their lives.
The Revolution was our first civil war, and in many ways it was much more bitter than our second one. Dissident Loyalists were treated far more harshly, for instance, than secessionists were in the WBTS, both during and after the war.
This was probably because Civil War I was a true civil war, brother against brother, while Civil War II was mostly a war between regions, except in the border states, where the fighting was the most bitter and the most atrocities took place.
That was not my statement. I just asked about the possibility of "Queen's" being in reference to Queen Elizabeth the First.