This is an example of a Courthouse Steps block.
Courthouse Steps is a variation of the Log Cabin block. Instead of piecing around the center square of the block, the piecing is done top and bottom and side and side as shown in the directions linked here.
Here is a pattern for a quilt made up of Courthouse Steps blocks. I linked it mainly so you could see the picture of the finished quilt.
As far as the history of Courthouse Steps and other Log Cabin variations, Barbara Brackman discusses how old the Log Cabin name is here. The only two alternate names I found for Courthouse Steps are Log Cabin (duh) and Judges (which I have admittedly only found in one spot.
I hope to get this cut tomorrow so that I can start piecing Monday or Tuesday!
Happy National Quilting Day!