Searched high and low and read a lot of documents/looked over some maps, but I can't seem to find anything about the history/layout of Mt. Vernon Square.
With as meticulously as Washington DC was planned out, it would seem that Washington Circle & Mt. Vernon Square should mirror each other (both circles or both squares). I would have thought it would be a circle, given the close proximity to the others in the area, but perhaps I'm missing something that prevented this from happening, i.e. existing structures.
Was this originally a circle (or supposed to be)? Is there any documented evidence as to why, during the planning, this area ended up being a "square?"
It was simply a design choice by Pierre L'Enfant, it was designed as one of the focal points of the city and designated a public reservation. It was originally just designated Reservation 8, the land plots are in the 800s there, and was intended to be developed later on. So it really held no specific attachment to what is now Washington Circle (Reservation 2) , it was simply named that after the are became known as the Mt. Vernon Neighborhood, before this it was known as part of the Northern Liberties, the area outside the more developed city.
The various historical societies and neighborhood itself have some nice information about the development of it.