Why does Megillas Esther spell Achashverosh's name varyingly with one (as in 2:21), two (as in 1:1), and zero (as in 10:1) letters Vav?
The Sefer Orah v’Simchah (cited here at Chabad) discusses the specific example of no vav’s in 10:1. He explains that
Public officials are highly lauded when they reduce taxes and criticized and scorned when they increase taxes. Not knowing Esther’s nationality, the King proclaimed an amnesty (from taxes) for all the provinces in her honor when he married her (2:18), thus enhancing his popularity with all the people. Now that he had levied taxes, he immediately lost some of their admiration and to indicate the decline in his popularity, his name is not spelled as fully as previously.
Perhaps we can extend this logic. His name is spelled with two vav’s consistently throughout the Megillah (no less than 24 times), as well as in Ezra 4:6.1 His name is only spelled with one vav in four places: 2:21, 3:12, 8:7, and 8:10.
2:21 is in the context of Bigsan and Seresh’s plot to kill the king:
ויבקשו לשלוח יד במלך אחשורש
And they sought to send hand against the king Achashveirosh
Clearly he’s a bit unpopular here. Perhaps he only loses one vav because it’s only a couple of people who don’t like him, rather than the populace at large.
3:12 is in the context of Haman’s decree:
בשם המלך אחשורש נכתב ונחתם בטבעת המלך
In the name of the king Achashveirosh was [the decree] written, and it was sealed with the signet ring of the king.
Here Haman is abusing his authority. While Achashveirosh acquiesced to the decree, Haman’s motive in asking for permission was to use him toward his own needs; since a decree signed with the king’s seal cannot be overturned, it’s in Haman’s best interests to get it signed that way. Since Haman is using the king for his own interests, rather than actually respecting him, the king loses a vav here as well.2
8:7 and 8:10 are in the context of the revision of Haman’s decree, that the Jews are now able to fight back.
Many of the populace hated the Jews and attacked any of them they could when the 13th of Adar finally rolled around. While the Pesukim indicate that 75,810 were killed in this battle (9:5-16), certainly there were many more who didn’t. Those who wanted to attack certainly wouldn’t have liked this new edict that the Jews could defend themselves (especially since they ended up dead as a result), but since the overwhelming majority did not attack — many of them, indeed, actually honored the Jews (9:3) — Achashveirosh’s name only loses one vav.3
In short: If only a minority, especially a tiny minority, dislikes the king’s actions, the name only loses one vav. But since nobody likes having their taxes raised, 10:1 drops both of the vav’s.
1It’s also spelled with both vav’s in Daniel 9:1. I’m not counting this one, though, as it’s in the context of his son, as דריוש בן אחשורוש.
23:7 uses the name in full, as it’s not referring to Haman’s interactions with him, just stating the year. 3:8 uses the name in full, as Haman wouldn’t dare to speak disrespectfully to the king in his presence. But in 3:12, when Haman is no longer in the king’s presence, Haman can show his true feelings.
3Yes, his name appears in full in 8:12, but since that refers to the countries, rather than the king himself, it doesn’t count, either.