How do they choose the names from which to name hurricanes and tornadoes?
Hurricane names are chosen well in advance. They are alphabetical and change each time from male to female names and the same names are reused time after time until one has been a major hurricane, any country affected by that storm may ask the World Meteorological Organization (WMO) to retire that hurricane name. Retiring a name means that it cant be used again for at least 10 years, to make references easier for many purposes such as, legal actions, historical reasons, insurance claims and to avoid confusion with another storm of the same name. So just check out hurricane websites to see if a future hurricane is likely to be your namesake.
Most answers are correct in terms of using the alphabet (not all letters are included, it is only a list of 21 names) and going in boy, girl, boy, girl order and then onto the greek alphabet if they run out of names. They only have so many lists of names which are used in rotation, with changes only made to a list if a hurricane was particularly devastating. This only applies to hurricanes in the Atlantic. For storms in other areas eg cyclones in Australia, they have different systems of naming. As for tornadoes, I don’t think they are given names, but are placed on the Fujita scale ie you will hear them referred to as F1, F2 etc.