When Levi was born, Leah said "This time my husband will become attached (yeloveh) to me". Then he called him Levi.
According to Midrash, Hashem named the boy Levi, because Levi was destined for the priesthood. The role of the priesthood is to take responsibility for increasing the closeness of our relationship with Hashem.
Rabbi Yaakov Kamenetsky, and Rabbi Wolbe said that Yaacov named the baby, and Leah heard it and realised he wanted to get closer to her. The word Levi connotes a true connection between people. See this page (upon which this answer is based) for examples. My favourite is Hashem was "mithalech" in the garden searching for Adam. Hashem seeks to forge a deep, intimate relationship of true Oneness with us!
Rabbi Chaim Goldstein states that the very essence of Levi is connection. Rabbi Chaim Shmulevitz says that their sanctity arisees from Levi's ability to create intimacy between husband and wife, and this became his shevet's mission in the marriage between Hashem and His people.
So as you can see, it's not (necessarily only) the merit of the man Levi, it's his destiny, a special feeling and powerful moment that took place by his birth. Don't underestimate the supreme importance of the closeness and intimacy between husband and wife.
Here is one possible merit of Levi himself, as noted in Shvilei Pinchas, based on the Chasam Sofer and the Vilna Gaon. When Yaakov designated Levi to be priests and spare them from the slavery of Egypt, Levi didn't want to just sit and watch his brothers suffer, so he named his sons with names that identify them all with suffering: Gershon = stranger, Kehot = broken teeth, Merori = bitterness. He taught us to empathise with the suffering of our brothers, and this was carried over to Moshe! Levi shouldered the load, Moshe shouldered the load, the Leviim shouldered the Ark!
A tribe destined to stand on the side, and be priests while the rest of Israel do the hard work of owning land, and raising the physical to the spiritual, needed to have this trait of being able to empathise and not be content to just sit and watch the suffering of their brothers, but share the burden. Levi instilled this in his tribe.
One of the 48 ways of acquiring Torah is
נוֹשֵׂא בְעֹל עִם חֲבֵרוֹ
Who shares in the bearing of a burden with his colleague