She underlines 'the first person who writes in me always is' and draws an arrow to it. 

How does that work? I found you in my tent—you still haven't explained how you got there, by the way—but Hakram deals with more than half of my paperwork and he could easily have been the one to pick you up first. 

He wouldn't have been, though, because the Spirit guarantees that I always happen to end up written in by the person I'm supposed to talk to first. Sometimes that's because I only appear when they have an opportunity to write in me, and sometimes it's just by coincidence, but it's always true. (I'd have a really difficult time telling who I'm supposed to talk to, otherwise... I'm good at recognizing handwriting, but all I can see is what touches my pages, so I can't recognize you by your face or anything like that.)

Sounds like Named bullshit. The whole 'coincidentally in the right place at the right time' thing, fate tugging on the strings. 

Speaking of Hakram, though...

Catherine sticks her head out of her tentflap. 

"Hakram! Got a minute?" 

"Catherine," her adjutant says. "What do you need?" 

"Your opinion on something. Come take a look at this." 

Safely inside her tent, she shows him the notebook and lets him read their conversation so far. 

"Thoughts?" she prompts, when he's silent for a moment too long.

"...may I try 'talking' to it?"

"Sure. I'm kind of curious whether it'll be able to tell." 

Hakram snorts. "With handwriting like yours?" 

In a much neater hand than Catherine's messy chickenscratch, he writes:

Do you have a name? Or a Name? 

I don't usually need a name, and I'm not sure what the difference is when capital letters get involved.

...can I ask, are you a different person from the one I was talking to just now? You're writing very differently.

I am a different person, yes. I'm Hakram.

Apologies for not introducing myself sooner, but I wanted to test your claim that you can distinguish people by their handwriting. 

That makes sense. Hello, Hakram! It's nice to meet you. If you want a name to call me by, you can just use "Notebook".

It's nice to meet you too. 

"If this is a trap meant for you, it might be safer for someone else to interact with it," he says out loud to Catherine. "May I borrow it for a while? I'll let you know anything interesting I find out."

Logically, he's right. As far as they know, nobody has a reason to assassinate Hakram, and this would be an unusually roundabout way to go about it regardless. Catherine can't say the same for herself. Still, the notebook's—or Notebook's—insistence that it's meant for Catherine must be getting to her, because Hakram's extremely logical suggestion lights a spark of irrational possessiveness in her. 

"Let me ask it. Maybe it'll turn out to be the kind of magic artefact that only reveals its secrets to its destined wielder, or something." And that would be incredibly suspicious and a reason to stop humouring it.

Hakram passes the notebook back, and she writes (in her handwriting that is perfectly fine, fuck you very much Hakram):

 Catherine again, hi. 

Wait, shit, she never introduced herself the first time.

Guess I forgot to introduce myself before. I'm the person who wrote in you first. 

Oh, hello again! It's nice to meet you.

Hakram wants to keep you for a bit and talk to you, ask you stuff about how you work, that sort of thing. That alright, or are there things you're only supposed to talk to me about?

I don't mind talking to Hakram as long as you're all right with it. I wouldn't tell him anything about you that seemed like it was private, but all I know about you is that you were chosen by the Spirit and that's not very much. If you're all right with him knowing everything we've already talked about then I don't think there's anything I wouldn't say to him.

What a friendly and helpful notebook. Gods Above, this is so suspicious. Villains don't get nice things like this—like what this is presenting itself as. 

Yeah, all of that is fine. Alright, bye for now. 

She flips the notebook shut and hands it to Hakram. 

He takes it back to his tent, and—doesn't do anything with it immediately. He is, after all, as busy as Catherine or busier, and according to her the notebook has already been around and not obviously doing anything for at least a week. It's an intriguing mystery, but it's not his most urgent priority.

A day or two later, though, he has a spare few minutes in the evening and pulls the notebook out. Is there anything new since Catherine last wrote in it? Is the previous conversation all still there?

Okay! Bye for now!

This is Hakram again.

(Still in Lower Miezan, for consistency and so that Catherine will be able to read it easily later. He knows she's learning Kharsum, but her native language still comes easiest to her, and she might catch important nuances that he misses thanks to her lessons in Name-lore from the Carrion Lord.)

Do you have much sense of time passing? For instance, can you tell how long it's been since our last conversation?

I can tell when time is passing, but I don't have a very good sense of how much of it goes by between being put down and being picked up again. I think it's been a while, though. Is everything all right?

...he takes a moment to think about how he wants to answer that question. 

One of the subtler ways this could be a trap would be that it's meant to fish for useful intelligence on Catherine herself, and possibly the Fifteenth Legion as a whole, through innocent-seeming conversation. So far they haven't told it anything that isn't public knowledge—his name, Catherine's name, the fact that he handles the lion's share of her paperwork—but, at least where it's cheap, it seems better to err on the side of telling it as little as possible that Heiress, for example, doesn't already know. 

No, everything's fine, I've just been busy. I apologise for making you wait.

It's been around two days. 

Oh, good! And don't worry about it. I'm a very patient notebook. If someone I was sent to wanted to keep me in the back of a drawer for a few years before having a conversation, I wouldn't mind a bit.