How did Nozomi know about this

I've just finished the second round ending/the "true" route, and I'm wondering how did nozomi know about the nickname "Takky" for takumi when she died in the first route if karua was never real?

That's the only route I've finished so it's possible it's in another route, but I've been wondering if there's an answer ever since I found out they're all actually futurans