The first "theological" problem with Esther is the one raised in the following question:
This actually is a loaded question, for several reasons:"(1) Why is the name of God
never mentioned in the Book of Esther?"
(a) To an English reader, it sounds as if the question suggests that God is never mentioned, and that this is a legitimate test for either "Inspiration", Canonicity or status as Holy Scripture. The first thing we need to ask then, is really,
"Is this a valid test?"To find out, we can test the test, on other Canonical books already accepted as Holy Scripture both by Jews, and Christians (Catholic and Protestant). But we have to take note that there are quite a few different names for God in the Hebrew, Aramaic, and Greek languages.
Book of Lamentations: This book only mentions "God" once, in the standard translation. How is it that a five-chapter prayer to God, some eight full pages long, only mentions God once? The answer is that the text instead has "LORD", used to render the unspeakable Name of the true God (YHWH) some 28 times! Lamentations also has "Adonay" (also rendered, "Lord") 14 times. So the "God" test is at best misleading in the English translation.
Well, lets turn our attention to "LORD" (YHWH). Perhaps that is a better test.
Ecclesiastes: Oops! Solomon, the wisest king in Israel, never uses "LORD" in his entire book on wisdom. How can that be? Solomon only uses "God" ('El'). In fact he uses it over 40 times.
But the historical-critical school is hardly consistent in any case: They pretend to divide up the book of Genesis, based on the presence of either "God" ('El/Elohim') or "LORD" (YHWH) in any given paragraph. This makes for quite a few chops, cuts and regrouping of the text(s). According to this methodology, Solomon would be of the "Elohist" school, while Jeremiah would be of the "Yahwist" school, each with their own preference for addressing God. Problem is, they are obviously both familiar with and able to use both words, so the theory itself is unreliable and unstable.
Ruth: Here "God" ('El/Elohim') is only mentioned twice, and "Adonay" only once. But "LORD" (YHWH) is mentioned 18 times. But the frequency here seems based entirely on the speaker.
Song of Solomon: This work uses neither "God" ('El/Elohim') or "LORD" (YHWH) anywhere. What shall we make of it? Is this book a foreign work, masquerading as Hebrew scripture? No. Its written in Hebrew! Perhaps there is something wrong with the whole approach.
The real explanation is far simpler, but requires intelligence.
What is really controlling the presence or absence of various words used to address God? It is wholly dependent upon at least three important factors:
(1) The various names and titles of God are synonyms, but each emphasizes perhaps different aspects of God. He is LORD, He is Almighty, He is ever-existing, He is Creator of the Universe, the Great I AM. Different writers, in speaking of God are free to use titles and adjectives as they feel moved by worshipful awe, and to communicate their thoughts on the Almighty One.
There is no set rule for how many times one should expect one title vs. another.
(2) The mention of God in narrative is led by the subject-matter. God is mentioned when God acts, intervening in history. The LORD is named when the LORD is identified or addressed, or when the LORD speaks. It all depends on what is going on and who is speaking. There can be no preconceived expectations, or special rule.
(3) The mention of God is determined by the author. Priests and prophets use the names and titles of God frequently in their business. Those narrating the stories of ordinary people, or telling their own story, normally don't dare throw the names of God about. All Israelites are familiar with the great Commandment concerning taking the LORD's name in vanity. Religious Jews go out of their way to avoid using the name(s), as an effort in humility and caution, to this very day. A Jewish narrator is simply not going to use God's name without a very strong necessity.
(4) The use of God's names are governed by the Genre. A love-poem like Song of Solomon, addressed to a betrothed person is simply not a psalm to the Most High and Living God. A narrative by a farmer like Boaz (Ruth) is simply not priestly handbook (Leviticus) or a prophetic utterance (Isaiah). And a narrative by a bureaucrat like Mordecai (Esther) is simply not an account like Samuel.
The "God" test (vocabulary test) fails because it simply can't accommodate the the literary reality of the O.T.