Having befriended a few actual drag queens several years ago, I found two methods of choosing names were prevalent (at least here in Los Angeles).
Method one consisted of making a pun out of a female sounding name, (not unlike the names of the girls in the James Bond movies). Examples are: Sophanda Peters, Huirlexin D'Ayre, Shih Go Daon Kwik, Ida Dunham, Eva Destruction, Hedda Lettuce, Lida Mae Honey and Helena Handbasket. This seems to be the most common method.
Another somewhat common method is the theme method. These drag queens joined families who take names with a similar theme. These themes can be geographical terms, foods or even ordinary adjectives, but are usually chosen to project an image of glamor or the exotic. Examples: Jamaica, Sierra, Indonesia and Malaysia J'atoi; Candy, Sugar, Honey, Cookie and Ginger LaCroix; Crystal and Jewel Arrington. The movie Paris Is Burning briefly explores a similar naming strategy.
Many Drag Queens do not fall into either category, and quite a few choose names they feel best represents their drag persona.