Learn Hardcore Korean: noteue je ireumi jeokhyeo isseoyo.

The particle 에 marks a static location and is broad: it can mean “in,” “on,” or “at” depending on context. With 노트에, it could be “in the notebook” (on its pages) or “on the notebook” (e.g., on the cover). Context clarifies the exact English preposition.

Why is 에 used instead of 에서 here?

에 is for a location where something exists or a state holds.
에서 is for the place where an action occurs. Because 적혀 있어요 describes a state (“is written”), not an action happening there, 에 is correct. Compare:
노트에서 제 이름을 적었어요. = I wrote my name in the notebook. (action)
노트에 제 이름이 적혀 있어요. = My name is written in the notebook. (state)

Why is it 제 이름이 and not 제 이름을?

The verb phrase is passive/resultative: 적혀 있어요 means “is written.” In passive/state descriptions, the thing that is written functions as the subject, so it takes the subject marker 이/가. If you used the active form (e.g., “I wrote my name”), you’d use the object marker 을/를: 제 이름을 적었어요.

Can I use 은/는 instead of 이/가 here? For example, 제 이름은…?

Yes, but the nuance changes:

제 이름이 적혀 있어요. states the fact and can introduce new information.
제 이름은 적혀 있어요. sets “my name” as the topic and often contrasts it with something else (e.g., “My name is written, but yours isn’t”). Use 은/는 when you want a contrast or topic shift.

What exactly does 적혀 있어요 mean, and how is it formed?

It’s a resultative passive meaning “is written (and remains that way).”

Base verb: 적다 (to write down)
Passive: 적히다 (to be written)
Resultative: 적히어 있다 → 적혀 있다 (“to be in the state of having been written”)
Polite present: 적혀 있어요 So it describes the current state resulting from a past writing action.

How is 적혀 있어요 different from 적었어요, 적고 있어요, or 적어 있어요?

적었어요 = “(someone) wrote (it).” Past action.
적고 있어요 = “(someone) is writing (it).” Ongoing action.
적어 있어요 is unnatural; for a state like this you need the passive plus -어 있다, hence 적혀 있어요 is the idiomatic form.

Is 쓰여 있어요 or 써져 있어요 also okay?

쓰여 있어요 (from 쓰이다) is fully standard and very common for “is written.”
써져 있어요 is widely used in speech and understood, though some style guides prefer 쓰여 있어요 in writing. Avoid double passives like 적혀져 있어요, which sound nonstandard.

Could I just say 노트에 제 이름이 있어요 without 적혀?

You can, and it means “My name is in/on the notebook,” simply stating existence. 적혀 있어요 adds the nuance that it is there specifically by being written (as opposed to, say, being on a sticker or printed label).

What’s the difference between 제, 저의, 내, and 나의?

제 = polite/humble “my,” the contracted form of 저의; most natural in polite speech.
저의 = very formal/literary “my”; acceptable but can sound stiff; in daily speech 제 is preferred.
내 = casual “my,” used with friends or younger people.
나의 = very formal/literary casual form; in speech, 내 is far more common. In this sentence, 제 matches the polite -요 style.

Should I use 성함 instead of 이름 to be more polite about my own name?

No. 성함 is an honorific noun used for someone else’s name. Referring to your own name with 성함 sounds self-elevating. Use 이름 for yourself. In very formal documents you might see 성명 for one’s own name.

Can I change the word order to 제 이름이 노트에 적혀 있어요?

Yes. Korean word order is flexible. Starting with 노트에 puts slight emphasis on the location; starting with 제 이름이 emphasizes the subject. Both are natural.

Why is there a space between 적혀 and 있어요? Should it be 적혀있어요?

Standard spacing treats -어 있다 constructions as two words because 있다 functions as an auxiliary indicating a resultant state. So write 적혀 있어요 (and in dictionary form, 적혀 있다). You’ll often see the no-space version in casual texting, but it’s not standard.

How do you pronounce the sentence naturally?

노트에: [노트에] (clear break; no special assimilation)
제: [제]
이름이: [이르미] (ㄹ-flapping of 르 between vowels)
적혀: [저켜] (ㄱ becomes aspirated [ㅋ] before ㅎ; 히어 → 혀)
있어요: [이써요] (the ㅆ is pronounced [ss], and ㅅ before ㅓ sounds like [s]) Full flow: [노트에 제 이르미 저켜 이써요]

Is there any difference between 노트, 공책, 수첩, and 메모?

노트: commonly “notebook” (school or spiral notebook). Also used for “notes” in some contexts.
공책: a school-style exercise book; slightly more textbook/native feel.
수첩: a small pocket notebook/planner.
메모: a memo/note (the content), not the book itself.

How do I make this negative, past, or future?

Negative (not written): 노트에 제 이름이 적혀 있지 않아요.
Past state (was written then): 노트에 제 이름이 적혀 있었어요.
Future likelihood: 노트에 제 이름이 적혀 있을 거예요. You can also ask: 적혀 있어요? to check if it is written.

Can I use 에다가/에다 here, like 노트에다가?

Use 에다가/에다 with active placement/writing to stress the target location: 노트에다가 제 이름을 적었어요. For the resultant state, stick with 노트에 제 이름이 적혀 있어요 (no 에다가).

Does 적다 also mean “to be few”? Is that related here?

Yes, 적다 has two unrelated meanings:

verb “to write down,” and
adjective “to be few/scarce.” Here it’s from the verb “to write down,” which forms the passive 적히다. The adjective meaning is unrelated in this sentence, so there’s no ambiguity.