Let's just say I have three Tamagotchi:
Hinotamatchi on v1
Tamatchi on v3
Pyonkotchi on v4
I connect v1 and v3 together. Version 1 does not have Tamatchi in its programming and Version 3 has Hinotamatchi in its programming. Therefore, Tamatchi appears as a Nazotchi on the v1 and Hinotamatchi appears normal on the v3.
I connect v1 and v4 together. Same as last time.
I connect v3 and v4 together. Version 3 has Pyonkotchi in its programming but version 4 doesn't have Tamatchi in its programming. Therefore, Pyonkotchi appears normal on version 3 but Pyonkotchi appears as Nazotchi on version 4.
One of the girls at school call Nazotchi "nut-man".
So basically if a character that you're connecting with is not in your Tamagotchi's programming, it'll appear as Nazotchi on yours.