Korach, Vayeitzei: Why Was Levi Called Levi?

From parshat Vayeitzei:

לד וַתַּהַר עוֹד, וַתֵּלֶד בֵּן, וַתֹּאמֶר עַתָּה הַפַּעַם יִלָּוֶה אִישִׁי אֵלַי, כִּי-יָלַדְתִּי לוֹ שְׁלֹשָׁה בָנִים; עַל-כֵּן קָרָא-שְׁמוֹ, לֵוִי.

34 And she conceived again, and bore a son; and said: 'Now this time will my husband be joined unto me, because I have borne him three sons.' Therefore was his name called Levi.

but towards the end of parshat Korach:

א וַיֹּאמֶר ה, אֶל-אַהֲרֹן, אַתָּה וּבָנֶיךָ וּבֵית-אָבִיךָ אִתָּךְ, תִּשְׂאוּ אֶת-עֲו‍ֹן הַמִּקְדָּשׁ; וְאַתָּה וּבָנֶיךָ אִתָּךְ, תִּשְׂאוּ אֶת-עֲו‍ֹן כְּהֻנַּתְכֶם.	1 And the LORD said unto Aaron: 'Thou and thy sons and thy fathers' house with thee shall bear the iniquity of the sanctuary; and thou and thy sons with thee shall bear the iniquity of your priesthood.
ב וְגַם אֶת-אַחֶיךָ מַטֵּה לֵוִי שֵׁבֶט אָבִיךָ, הַקְרֵב אִתָּךְ, וְיִלָּווּ עָלֶיךָ, וִישָׁרְתוּךָ; וְאַתָּה וּבָנֶיךָ אִתָּךְ, לִפְנֵי אֹהֶל הָעֵדֻת.	2 And thy brethren also, the tribe of Levi, the tribe of thy father, bring thou near with thee, that they may be joined unto thee, and minister unto thee, thou and thy sons with thee being before the tent of the testimony.

Thus, the kohanim, descendants of Aharon, are so called because of their function of ministering. (Elsewhere, the Netinim are given over to serve, and are so called because of their function.) And the typical Levites are joined unto the kohanim, to minister under them -- וְיִלָּווּ עָלֶיךָ. And two pesukim later:

ד וְנִלְווּ עָלֶיךָ--וְשָׁמְרוּ אֶת-מִשְׁמֶרֶת אֹהֶל מוֹעֵד, לְכֹל עֲבֹדַת הָאֹהֶל; וְזָר, לֹא-יִקְרַב אֲלֵיכֶם.

4 And they shall be joined unto thee, and keep the charge of the tent of meeting, whatsoever the service of the Tent may be; but a common man shall not draw nigh unto you.

This appears at first glance to be another instance of dual etymology. Even though in both cases the root is the same, the question is who is joining. In Vayeitzei it is Yaakov who will join her, while in Korach it is the tribe, such that perhaps they are so called because of their function.

This is readily dismissible, if need be, as a simple pun in parshat Korach, drawing on Levi's name to describe shevet Levi's role, something which the Biblical text frequently does.