(As of 2019 the API is apparently returning "no content" to many names that are actually taken. This means the script will think the name is available, even though it isn't. This greatly reduces the utility of this script. If you know of a way around this issue, you're welcome to try to address it.
Until then, for a similar and more reliable service, you can use namemc: https://namemc.com/minecraft-names?length_op=eq&length=3&lang=&searches=0)
This is a small clojure script that queries the Minecraft API to test for all available 3 character names.
The found playernames are in available-now.txt (currently available names) and soon-available.txt (not currently in use but still under the 37 day protection.) Do note that these lists are NOT automatically updated, but instead show which names were available when the script was last run. If you've got a newer copy of these lists, feel free to submit a pull request.
The without-numbers files can be generated with
grep "^[a-z]*$" available-now.txt > available-now-without-numbers.txt
grep "^[a-z]*$" soon-available.txt > soon-available-without-numbers.txt