Locally here near South Hill, VA we have a hamlet named Union Level.
As I drive to Richmond on Rte. 95 I pas an exit for Squirrel Level
Road. No one here that I can find seems to know about the origin of
Union Level. I just discovered Squirrel Level the other day and
wouldn't even dare guess. I am asking what is the origin of the use of
the word "Level" in geographic names?

According to the American Heritage dictionary "Level Crossing" is a
British term for a grade crossing.  And a "Grade Crossing" is a
intersection of roads, railroad tracks, or a road and a railroad track
at the same level.

The normal geographic use of 'level' is to refer to an area of (vary) flat land.
This is often used in place names where the land has clear boundaries,
for example a river/canal/drainage system.

"Union Level" as a name could suggest that the settlement was founded
after the Civil War  (Sorry -  War between the States.  I grew up in
Ala. back when), by folks with a more positive attitude to the war's
outcome than maybe the older Virginians had.
Sure, everyone is right:  "level" is just that, a more flat area;
plateau, on a hillside, in a valley.
Now if there is  - or were once -  a train station at Union Level, the
"union" could indicate that it was served by two or more railway
companies.  This is the origin for the name of Union Station in Wash.
DC and elsewhere.