I say twin, you say doppelganger
The more syllables you use to say the same thing, clearly the cleverer you are and the more serious you are about the issues.
Unless they are trying to say that the way forward, to avoid *accidentally* mixing their data, is to just smoosh them all up: make all the "John Smiths" perfectly the same, proper doppelgangers.
PS
Don't these government agencies bother with, you know, simple ways to tell two people with the same name & d.o.b. apart? Even though I'm pretty sure I'm the only Corner in the Village (ovoid architecture, very popular around here) I still get asked "what is the first line of the address?". If that failed, at least I'd be aware of the potential problem (hosting a clan reunion that had gone on just a bit too long) and could nudge the government agent.