Belgium's national register number is similar:
YY.MM.DD-AAA.BB
In either the AAA or BB component there is something about the gender.
But it does mean that there is a limit of people born per day of a certain gender.
But for a given year, using a moniker will only delay the inevitable. Sure, there are more numbers, but still limited as there are SOME parts that need to reflect reality. Year, gender (if that's still the case?) etc.
BB is a mod-97 checksum. The first A of AAA encodes your gender in an even/odd fashion, I forgot if its the first or last A doing that. MM or DD can be 00 if unknown. Also MM has +20 or +40 in some cases.
If you know someones birth date and gender, the INSZ is almost certainly 1 in 500 numbers, with a heavy skew to the lower AAA. Luckily, you can't do much damage with someones number,unlike an USA SSN (but I'd still treat it confidential).