This needlepoint filling stitch goes by the name of either the Checkered Mosaic Stitch, or the Mosaic Checker Stitch, and is made from blocks of a single Mosaic Stitch alternating with blocks of four tent stitches.
It can be worked in a single color, in 2 colors as shown here.
This stitch was used in the Chunky Spring Birds project.
The link to print the Stitch Journal page can be found in Step 3.