Earlier quoted context omitted.
There was a proposal going around the Lib Dems in the UK at one point[1] to make it illegal to have names on CVs; because they describe gender, and sometimes race, too. The proposal went on to say that that people should apply for jobs using their National Insurance number (like a social security number, but basically just used as a UID with the tax office - I don't know what else a SSN does, but it seems to be more…
It won't work everywhere; e.g. SSN equivalent in Poland has sex encoded as one of the digits (determined by whether it's even or odd).
It could be a hash of the persons name, too, but then the public would have to learn what a hash was...
NI number works well in the UK, because it's convenient (and the original suggestion was specifically for the UK.) A similar system could be used anywhere.