Charles Ellicott Commentary Numbers 17:3

"And thou shalt write Aaron`s name upon the rod of Levi; for there shall be one rod for each head of their fathers` houses." — Numbers 17:3 (ASV)

And thou shalt write Aaron’s name upon the rod of Levi. —Aaron was descended from the second son of Levi. He was not, therefore, the natural head of his father’s house, but the divinely-appointed one, and for this reason it would not have been sufficient for the intended purpose to have inscribed the name of Levi upon the rod. Aaron was appointed the head of both the priests and the Levites, the two classes into which the tribe of Levi was divided.