for popular sites, any good name has long been taken. so I just find the shortest one possible. Have to be careful though. for example, with Hacker News, better to check:

https://news.ycombinator.com/user?id=hello

than here:

https://news.ycombinator.com/login

because the second option, they will IP ban if you request more than once every 8 seconds. here are some open ones, I got tired of waiting so its not a full list:

0c 0e 0g 0i 0l 0n 0r 0s 0u 0v 1b 1f 1g 1h 1l 1n 1o 1t 1u 1w 1y 1z 2g 2i 2l 2o 2p 2q 2r 2s 2u 2w 2x 2z 34 35 38 3b 3c 3g 3h 3j 3k 3m 3o 3p 3q 3r 3s 3u 3w 3y 4b 4c 4d 4e 4f 4h 4i 4j 4l 4m 4o 4q 4r 4s 4v 4x 4y 4z 54 5a 5b 5c 5e 5i 5j 5m 5o 5p 5q 5r 5s 5t 5u 5w 5x 5y 5z 62 67 6b 6e 6h 6i 6j 6k 6l