The test of the staffs was designed to finally settle the question of spiritual leadership among the Israelites and quiet their ongoing complaints. To ensure complete fairness and credibility, a single piece of wood was taken and divided into twelve identical pieces. This meant Aaron's staff was exactly the same as the staffs of the other tribal leaders, making the miracle that followed absolute and beyond dispute [אור החיים, שד״ל]. Unlike the military censuses, where the tribe of Levi was kept separate and the tribe of Joseph was divided into two, this test reflected the original structure of the Israelite tribes. Here, Levi was included as an integral part of the twelve [ביאור שטיינזלץ, אור החיים].
Aaron's name was written on the staff of Levi because he served as the tribe's main leader and representative [ביאור שטיינזלץ, ביאור יש״ר]. Even though the tribe of Levi had other leaders appointed over its various families, only Aaron's name was recorded, as he was the chosen individual from the entire group [מלבי״ם]. At this point, the test was not meant to prove Aaron's personal right to the priesthood over other Levites, as that issue had already been resolved through the punishment of Korah. Instead, the goal was to prove to the rest of the tribes that the entire tribe of Levi was chosen by God, with Aaron standing as their representative in this public test [פענח רזא].
The primary approach among commentators is that the specification of a single staff for the head of the tribe was meant to prevent a misunderstanding. Because the tribe of Levi was divided into two distinct groups with separate roles, the Priests and the Levites, one might assume they required two separate staffs. However, despite this internal division, they were still considered a single tribe under one leader, making one staff sufficient.
Beyond this practical detail, there is a deep message about the unity of the tribe. The priesthood is not separate from the rest of the tribe; rather, it is the highest and most complete expression of it. While the Priests form the elite group, the tribe remains a single, indivisible entity [רש ר הירש]. This unity is further highlighted by the miraculous signs that would eventually appear on the staff. The flowers, which symbolize the priesthood, and the almonds, which symbolize the Levites, would bloom together on the exact same branch. Their shared appearance on a single piece of wood proves that both roles are deeply connected, rely on one another, and come from the exact same source [העמק דבר].