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?

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.

@Lensflare I also live in Germany but was born in a small village in a foreign country. Back then, when I requested a passport, the women behind the desk asked me how to spell the name of the village. I didn't know, so I just came up with a spelling. Now I know a few other people from that village - it's completely differently spelled in their passport.

Also birthday is something nobody can prove. I can come up with a slight variation or pick another one.

I think the trickiest part is to make someone believe that you lost every document and you are not in "the system" yet.

Well, at least in Europe, your identity is your national id document. Whatever is there, flies.

You can't have two, well, because you can't. You can modify your current one, sure, but that's it.

At least in Spain, even if you claim theft or loss, they'll check your fingerprints again and find out.