On her website, Stephanie Meyer discusses the difficulty in the title of the first book of the series, Twilight. She says it was on a list of "words with atmosphere" that both she and her agent liked. Though she admits that she isn't sure it was the best title for the first book of the series, it seems that once she went with it, she decided to carry the moon symbolism throughout. There are those who believe each book is appropriately symbolically titled to fit Bella's journey throughout the four books. Twilight for example, happens just as the day is ending and the night is beginning. It is the beginning of the safest time for Edward and the others to be out, just as it is the beginning of Bella and Edward's relationship.
A new moon is of course, the absence of a moon which creates the darkest of nights. New Moon, even according to the author, is a book about Bella's darkest time.
It is only logical then, to consider the symbolic implications that come with an eclipse. An eclipse, first of all, is very rare. It is the total or partial obscuring of one celestial body by another. Simply put, the earth, sun, and moon must be lined up in such a way that a moment of raw scientific beauty takes place. The title Eclipse could refer to the rare aligning of events that allowed Edward and Bella to come together. It could also refer to the love triangle between Edward, Bella, and Jacob, where the presence of one is obscuring another.