Not to worry
There are 24 letters in the Greek alphabet. Hurricane season "officially" ends November 30 -- 33 days from today (although the actual end depends on the weather in East Africa, the shear force of high-altitude winds over the mid-Atlantic, and ocean temperatures).
Since Alpha and Beta have been assigned, that leaves 33/22 -- in other words, one tropical storm strong enough to receive a name every day and a half, beginning today, for the rest of the season -- just to run out of Greek letters. Even this season hasn't been that crazy... has it?
In the future, however... maybe they'll go to the military phonetic alphabet if they run out of Greeks.
hmmm.... Hurricane Foxtrot?