If they are bad enough?
See this recent thread.
Yes, they can be retired. However, the official name of the retired storm is the name, and the year. So if Alpha had done enough damage to worthy a retirement, the retired storm name would be Alpha-2005, and Alpha would be free to be used the following year.
Hmm, the other thread includes a cite that there currently isn’t any provision for retiring Greek names. And retiring “Alpha-2005” is, well, a silly idea, because it’s not like “Alpha-2005” is ever going to be used again, so if they use the name “Alpha” again, it’s effectively not retired at all, and will still have the same negative connotations if it were to be reused.
According to this news story one of the Greek names (alpha) may be retired after this year. From what I can tell from NOAA’s Hurricane Name site there is no year designation added to a retired name, once it is retired it won’t be used again. I read an article earlier in the season about what to do if the Greek alphabet is ever exhausted (no cite i’m afraid, I could not find it) and it said that the Greek letters would not be replaced as retired (Beta could be the 22nd huricane next year if Alpha is retired) but if the letters are all exhausted another alphabet would be used, the article suggested Swahili 
.
If we run out of Chinese characters, it’s time to move away from the Gulf Coast.
Hopefully, that suggestion is in jest, as Swahili used the Roman alphabet. So we’d be saying “Hurricane A”, “Hurricane B”, etc.
Corrected.
OK, I’d like to correct my earlier assertion. Seems several people on message boards I frequent regarding hurricanes stated the retiring name as Alpha-05 as fact, but I could find no mention anywhere else.
So while it may be true, there is no evidence yet that I can find. Maybe the WMO conference next year may end the confusion.