Megillath Esther is a canonical book (i.e., in the biblical canon) about the salvation of the Jewish people. Why, then, doesn't G-d's name appear anywhere in the text?
The Ibn Ezra in his introduction to Ester answers that the book of Ester was originally part of the Persian chronicles, but the Persians attributed it all to their god's name rather than to ours; so when Mordechai wrote the book of Ester copying it from the Persian chronicles, he erased the name of their god, so his not mentioning God's name was actually out of honor to God.
An interesting theory is that it was intentionally omitted to call attention to the Pur/chance related theme which conflicts with Jewish belief and how that belief was upended.
The holiday of “Purim” itself is named after the lots (purim in Akkadian) that were cast to determine the fate of the Jews (see Esther 3:7). As such, by not mentioning God it seems to offer proof for the theory that life — its political machinations, its causes and effects, its outcomes, etc. — is chancy, and is rooted in “the throw of the dice”. After all, there doesn’t seem to be a purposeful, omniscient, and omnipotent being anywhere to explain it.
What we people of faith believe, though — based on the thinking and ruminations of the best of us, to say nothing of direct revelation — is that the best theory of all behind everything that happens here is in fact the existence of just such a Being, God, who, while hidden, is still behind it all. So while not offering that theory itself the Book of Esther was included in Tanach to underscore the idea that God does indeed control life’s machinations, and that belief in Him is in fact the most viable theory of all.