"Shoo-Fly Pie" is a very sweet pie made with molasses. It may have gotten its name because flies were attracted to pools of molasses that often formed on the pie surface while it was cooling, and had to be "shooed" away.
"Apple Pan Dowdy" (or pandowdy) was probably given this name because the dessert looks plain or "dowdy". The apple based filling is placed on a crust, and the top crust is broken or sliced through several times. It is very juicy served hot from the oven. As it cools, the "dowdied" crust absorbs a lot of the liquid. It can be eaten warm or cooled.
In 1945, "Shoo Fly Pie and Apple Pan Dowdy" was published as a song. It was recorded by Dinah Shore and by Ella Fitzgerald.