The Me’am Loez writes that they decided on the name of the holiday being Purim because the lots being rolled in Nissan, and coming up with the date in Adar eleven months later gave the Jews time to pray and to repent.
Furthermore, Adar had previously had no other holidays, so Purim’s falling out then made it stand out more conspicuously as a holiday, receiving the attention it deserves.
Also, the Vilna Gaon and Malbim point out that the lots pointed to a potentially bad fortune, but H-Shem reversed it to a good fortune.
In quoting Rabbeinu Yona’s Shaarei Teshuva (2:4), the Ginzei HaMelech notes that just as sin can be transformed to a mitzva status if the sin leads to teshuva (“repentance”), so too the lots lead directly to the Jews’ redemption.
The Ksav Sofer supports this point by writing that in calling the day Purim, we celebrate the pain suffered by the Jews at this time, since it led directly to their re-acceptance of Torah (Esther 9:27).
Rav Moshe Feinstein wrote that the message to be learned from this is that one should never overconfident of one’s “lot,” thinking that one’s greatness in Torah knowledge or observance will necessarily parry off the Evil Inclination. Rather, even such a person should be always mindful of one’s potential to fall prey to one’s natural, animalistic urges.