I believe the oft-cited reason for God’s name not being found in the book of Esther is that this would have been an unpopular thing to be found in “Persian” literature. However, this does not explain why the second highest in command, Mordecai, and his adopted daughter, Esther, cannot, from their positions of power, say, “We were delivered by the God of Israel and our feast of Purim is dedicated to Him.” Given their position of power and given the strength of the Jews who had just “delivered themselves” by their own weapons, holding forth their God would be something we would expect.
The book of Esther essentially deals with Jews living among gentiles in a gentile country. It is a shadow of what is to come. It emphasizes that, no matter how much the Jew integrates himself into society, he always remains a Jew, and is always a target for Satan’s machinations. The primary concern of the Jews living in a gentile country is not the land which has been given them; nor is their primary concern the God who formed them; their primary concern is with their life within that gentile country. Although the Jews who we observe, Esther and Mordecai, seem like people who are noble and grounded in the laws of establishment, we cannot say beyond a shadow of a doubt that either one is a believer in Jesus Christ. Even though it is clear to us as believers that God is preserving them, it is not obvious that they realize that God is preserving them. It is equally probable that they are left with the trappings of their religion, without the core of their faith, Who is Jesus Christ—just like the Jews today. Mordecai knows enough not to bow down to Haman, but Mordecai does not know before Whom he should bow. This is why we see fasting, but no prayer; this is why we have a celebration of deliverance, but no mention of a Deliverer.
The book of Esther foreshadows the Jews of today, scattered in gentile countries, the prey of Satan, and who are delivered by Jesus Christ again and again—delivered by Jesus Christ, their God, even though they do not, as a whole, recognize Him as God. Sometime in the future, the Jews will read Esther and say, “Where is God? Why don’t we know Who God is in this book? Why don’t we turn to God in this book? Why is God so clearly delivering us, but we do not acknowledge that He has delivered us?” In fact, I believe that many of the 144,000 Jews will be evangelized by the book of Esther. They will read Esther, or hear it read, and their hearts will be struck with, “This is us today! We do not know Who God is; we do not recognize the God of Israel. We are clinging to a plethora of laws, but not to the God Who formed us.” It is a relatively short step from here to faith in Jesus Christ.
Now the only problem with this explanation is that we know many Persians became Jews, which we understand as these Persians becoming believers. This can be approached from two positions: either they simply married Jews and adopted their ways and laws or they did become believers through their association with the Jews. Both are probably true. There are Jewish believers today, albeit a small percentage, and many are converted by God through these believers (a modern example would be the group Jews for Jesus).