Although Hashem’s name is not mentioned explicitly in the Megillah, the holy seforim say that whenever it states the word, המלך, alone in the Megillah, (not two words like המלך אחשורש) it refers to Hashem, the King of the world.
The Maharal says that, המלך, isn't only hinting at “the King, Hashem.” המלך in the Megillah means Hashem. Proof of this is in the words: בלילה ההוא נדדה שנת - “That night, the king's sleep was disturbed.” The Gemara (Megillah 15b) cites a machlokes [dispute] regarding the translation of המלך in this pasuk. According to Rav Tanchum, המלך, is Hashem, for He is the King of the world. The pasuk is saying that keviyachol [so to speak], Hashem, couldn’t sleep because it was time to save the Jewish nation. So, we see, according to Rav Tanchum, that the simple translation of, המלך, is the King, Hashem. We think that Achashveirosh or others were pulling the strings and causing events to happen, but, המלך, is our reminder that everything is from Hashem.
This is the message of the Megillah, to know that Hashem is with us and performs miracles for us within the rules of nature. The first Mishnah in Megillah states, "The Megillah is read on the 11th, the 12th, the 13th, the 14th, and the 15th [of Adar], not later and not earlier.”
The Bris Kehunas Olam writes that the total of these dates equals 65 (11 + 12 + 13 + 14 +15 = 65), the same as אדנ"י . The name אדנ"י is Hashem’s name when He runs the world by the rules of nature. We read the Megillah on these dates, which are gematriya אדנ"י, because the purpose of the miracle is to know that even a world run by nature is led by Hashem.
The Mishnah adds: לא פחות ולא יותר – “Not earlier and later”. This means we can only read the Megillah on the aforementioned five dates, not the day before or after. The day before is the 10th of Adar, and the day after is the 16th, together the gematriya is 26 (10 + 16 = 26), the gematriya of הוי"ה, Hashem's name for miracles. We can't read the Megillah on these days because on Purim, we aren't celebrating the revealed miracles, which are symbolized by Hashem's name הוי"ה. On Purim we celebrate that even when everything appears natural, Hashem is with us, directing each detail.
