Do you think it would be possible, to create a second real identity (acknowledged by government) by using the real name, but switching some or even just one of the letters with a unicode look-alike character?

lots of people have the same exact name

it is unknown how a person is represented inside "government". social insurance / social security numbers seem to be relevant even though when they were made it was explicitly said they shouldn't be used for authentication, but now they serve as a sort of password only you're supposed to know (except you have to give it to your employer lol, and MLMs and scam jobs exist so make that make sense)

If the name already exists then they will use your birthdate and birth location and will know that you are the same person.

Your name is not your identity.