I know several people who went through this process, and it's not pretty. Besides the bureaucratic hassle, some systems, particularly in the medical sector, are just straight up not designed to handle those kinds of changes. Almost everything healthcare-related here is tied to your PESEL and spread through dozens of different databases (and possibly paper files) which are hard to impossible to modify. I've heard of vaccination info being lost, prescription fulfilling issues and the ePatient portal straight up refusing to work with strange errors. Apparently for some banks, the recommendation used to be to close your account and just go to another bank which never saw your old data, although that has now gotten better as far as I know.