Shizune explains about the missions

"Actually, Koyuki Kazahana is asking for you to escort her on a diplomatic trip to few countries."

"Why me?"

"She knows you personally, and on our side, you're one of our most traveled shinobis."

Now it makes sense why Shizune mentioned her name out of the blue. Even if it wasn't intended, Shizune mentions her name in the prior conversation because Koyuki is in her mind; the princess is nominating you, a Konoha shinobi to escort her. "This is that diplomat mission, isn't it?"

Shizune nods in affirmation.

Another name that she mentioned is Temari. "So if I choose the west patrol, I take it that it will be with a Suna team?"

"Not really. You'll do it with Kankuro and Temari. But that's amazing! How do you know about that?"

"Oh, a little guess work," you say modestly. "So, why are you telling me about the missions?"

"Well, they're not really classified. On the other hand, giving you the option of meeting someone you know is a good thing. But if you want to chose one of those two, we have to return back to the tower as the missions are time-limited."