Looks like there's some bugs here. Just claimed 'esi' was available on Twitter and GitHub, but it's not.
Edit: Just to be sure, I threw in a breakpoint on line 18 of generate.js, and set name to my username (cbhl) -- and got a false "free" result for both Twitter and GitHub.
The OP might need to be getting OAuth tokens and using the GitHub/Twitter APIs.
edit: just realised you meant that twitter/github etc are rate limiting my requests. Bummer.
Not quit the same (a username might be reserved internally), but either way, nobody else can use the name.
Otherwise, I'd say you're probably out of luck. (You could try doing the query over IPv6, but eventually they'll just block the entire subnet, so I don't know if it's worth the trouble.)