The funny thing about that squadron patch is that the design comes from an old E-2C Hawkeye squadron, VAW-110. :-D It was the FRS (training squadron) on the west coast while Miramar was still operated by the Navy. After the base was transferred to the Marine Corps, VAW-110 was absorbed into the east coast FRS, VAW-120. VAW-120 uses the same design for its squadron patch, but with different colors. The blue background, red border lines, and lettering are changed to black, and the bird is gray instead of red.
Incidentally, Navy aviation people typically wear the flag patch on the left shoulder, and the squadron patch usually goes on the right side of the chest. The name tag goes on the left side of the chest and a patch of the person's choice goes on the right shoulder.