Eönwë's name derives from an earlier form Fionwë. Its meaning isn't just 'unknown' in the sense that its meaning is never explained. Rather, Tolkien himself stated that no Elvish etymology was known, hinting that it derived instead from the native language of the Valar and Maiar.
Apparently in contradiction to this, however, the name Fionwë is mentioned in The Etymologies (in volume 4 of The History of Middle-earth), where it is said to derive from the word fion. Unfortunately the meaning of the word is not precisely legible: Christopher Tolkien gives the most likely reading as 'haste', with 'hawk' also a possibility.