sono syorui no hyousi ni namae wo kakanai to, dare no mono ka wakarimasen.

Yes. In this sentence, 書かないと means if you don’t write.

Here, と is a conditional particle. It connects two parts like this:

• 書かない = do not write
• 書かないと = if you do not write

So:

• 名前を書かないと、だれのものか分かりません。
• If you don’t write the name, we won’t know whose it is.

This と often sounds like a natural result, consequence, or warning:

• 春になると、桜が咲きます。 = When spring comes, cherry blossoms bloom.
• 急がないと、遅れます。 = If you don’t hurry, you’ll be late.

In this sentence, it gives the feeling: if you don’t do this, this problem will happen.

Because に marks the place where something is written.

• 表紙 = cover
• 表紙に名前を書く = write a name on the cover

With verbs like 書く, the thing being written takes を, and the surface/location often takes に:

• 名前を書く = write a name
• 表紙に書く = write on the cover

So in this sentence:

• その書類の表紙に名前を書く
• write a name on the cover of that document

It means the cover of that document.

Breakdown:

• その = that
• 書類 = document / papers
• の = of
• 表紙 = cover

So:

• その書類の表紙
• literally: that document’s cover
• natural English: the cover of that document

The particle の links nouns together. It often works like ’s or of in English.

Because Japanese often leaves out information that is obvious from context.

In this sentence, 名前を書く naturally means write your name. There is no need to say your if the situation already makes it clear.

So:

• 名前を書く = write your name / write a name

Depending on context, it could theoretically mean someone else’s name, but here the intended meaning is clearly write your own name.

Japanese often omits:

• subjects
• possessives
• objects

when they are understood.

Here, か marks an embedded question.

Compare these:

• だれのものですか。 = Whose is it?
• だれのものか分かりません。 = I/We don’t know whose it is.

So か is not asking the listener directly. Instead, it turns だれのもの into a clause meaning whose it is.

You can think of it like this:

• だれのもの = whose thing / whose it is
• だれのものか = who it belongs to / whose it is
• だれのものか分かりません = I don’t know whose it is

This is very common in Japanese:

• 何をするか決めました。 = I decided what to do.
• どこへ行くか分かりません。 = I don’t know where to go / where someone will go.

だれのもの literally means whose thing or the thing belonging to whom.

• だれ = who
• の = ’s / of
• もの = thing

So:

• だれのもの = whose thing / whose one

In many situations, Japanese can also use just だれの if the noun is clear from context. But だれのもの is very common when the noun is omitted and you mean whose it is.

For example:

• これはだれのものですか。 = Whose is this?
• これはだれのですか。 = Whose is this?

Both can work, but だれのもの can sound a little fuller or more explicit.

Because 分かる is often used for understand / be clear / be معلوم / be known, while 知る means to know in the sense of to have knowledge of something.

In this sentence, the meaning is closer to:

• we won’t be able to tell whose it is
• it won’t be clear whose it is

So 分かりません is the natural choice.

Compare:

• 彼の名前を知りません。 = I don’t know his name.
• これは何か分かりません。 = I don’t know what this is / I can’t tell what this is.

Here, the issue is not stored knowledge; it is identifying ownership from the situation. That is why 分かりません sounds right.

Japanese often omits the subject when it is obvious or not important.

So 分かりません could mean:

• I don’t know
• we don’t know
• people won’t know
• it won’t be clear

depending on context.

In this sentence, the natural English translation is often:

• If you don’t write your name on the cover of that document, we won’t know whose it is.

But it could also be understood more generally as:

• ...it won’t be clear whose it is.

Japanese leaves that flexible.

They are similar, but not identical.

1. 書かないと

Means if you don’t write and often suggests a natural consequence or warning.

• 書かないと、分かりません。
• If you don’t write it, we won’t know.

2. 書かなければ

Also means if you don’t write or unless you write, but it can sound a bit more formal or written depending on context.

• 書かなければ、分かりません。

3. 書かないなら

Means more like if you’re not going to write it or if it is the case that you won’t write it. It often depends more on someone’s choice or decision.

• 書かないなら、分かりません。
• If you’re not going to write it, then we won’t know.

In your sentence, 書かないと is very natural because it expresses a straightforward result.

Because the whole sentence is in polite style.

• dictionary/plain form: 分からない
• polite negative: 分かりません

Japanese often keeps the style consistent across the sentence. Here, the speaker is using polite language, so the sentence ends politely.

Notice that the earlier part is still 書かない, not 書きません, because in conditionals and subordinate clauses, plain forms are commonly used even in polite sentences.

So this is normal:

• 書かないと、分かりません。

not strange at all.

Because だれのもの is the standard way to say whose.

• だれ = who
• だれの = whose

So:

• だれのものか = whose it is

Using どの人 would sound unnatural here, because English whose is normally expressed in Japanese with だれの.

Examples:

• これはだれの本ですか。 = Whose book is this?
• あのかばんはだれのものですか。 = Whose bag is that?

Yes, definitely.

Although the literal structure is just conditional, the sentence can sound like a practical warning or instruction:

• If you don’t write your name on the cover of that document, we won’t know whose it is.

So the speaker may really be implying:

• Please write your name.
• Make sure to put your name on it.

This is common in Japanese. Instead of directly ordering someone, the speaker explains the consequence. That can sound more natural and less blunt than a direct command.