Moûsa

Several hypotheses exist:

From *Μονθια (*Monthia), from Proto-Indo-European *men- (“to think”) + *dʰeh₁-, whence μανθάνω (manthánō).
From *Μοντια (*Montia), from Proto-Indo-European *men- (“to tower; mountain”), since all the most important cult-centres of the Muses were on mountains or hills, ^[1] but Beekes finds this etymology impossible, as the root mont- 'mountain' from IE *men- is not found in Greek.
From Proto-Indo-European *mō-, *mē- (“endeavour, will, temper”). Cognate with μῶμαι (mômai, “to seek after, meditate”), μαίομαι (maíomai, “to seek after”), μαιμάω (maimáō, “to be very eager”), Latin mōs, English mood, Proto-Slavic *sъmě̀ti.
Beekes suggests the possibility of a borrowing from Pre-Greek.
Swerdlow^[2] traces it back to Bohairic Coptic Egyptian mōw—apparently cognate with Hebrew משה, Moses—medieval sources mentioning that, like the prophet, “music was found by the water.”

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Μοῦσᾰ • (Moûsa) f (genitive Μούσης); first declension