Excerpt from Asher Intrater:

When Jacob married Leah, his third son was Levy.  His name came from Leah’s saying that her husband would “closely accompany” her – Genesis 29:34.  This is the root of Levy לוי.  Leah meant this in a soulish way, but God – in His sovereign election of this family – used the name to achieve a spiritual destiny.  Those who became the priestly tribe, took the name Levy as one who “clings to,” “joins to,” “closely adheres to,” or “accompanies” the Lord.

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