My impression by living in NZ for a while now that I can call myself anything I want.
I've been asked to verify my identity only when setting up bank account, sorting out visa/tax with my sponsoring employer. After that it's only when leaving/entering country.
For my own convenience I use an english name to save barista butchering my name and feeling bad about it.
Naming kids was an exercise in linguistics. In Lithuanian we have some fun accidents like Justinas (just in ass) and Arminas (arm in ass)...