How many asteroids are named after musicians? Is there a searchable list for this? Spot checking Wikipedia, Google and JPL's Horizions I found several musicians right away, including Lou Reed, Elvis, Freddy Mercury, and David Bowie.

Is there a way to find all of the asteroids that are named after musicians somehow? Or at least most of them? If there's not a compiled list, at least something for which an automated search for "music" or "musician" or related terms can be done?
I don't think you can do better than search the wikipedia pages, where there is a list https://en.wikipedia.org/wiki/List_of_minor_planets_named_after_people. Or you can search yourself through https://en.wikipedia.org/wiki/Meanings_of_minor_planet_names, if you don't trust wikipedian's curation

But you may need to be quite subtle about how you search, since searching for "music" won't find those that are described as "composers", nor those who are "sopranos", or "violinists" and so forth.  There are also edge cases. William Herschel (who may have coined the name "asteroid") was also a classical composer of note. Or "644 Cosima", named after Wagner's second wife.  How about 1683 Castafiore, named for a fictional "musician"?