Я записал его имя в блокнот.

Записал is the past tense, masculine singular form of записать.

Here it means wrote down, noted, or recorded.

A few important points:

• за- is part of the verb and helps give the sense of writing something down
• -л marks the past tense
• the form записал shows the speaker is male

So:

• Я записал его имя в блокнот = a male speaker
• Я записала его имя в блокнот = a female speaker

Because Russian often builds that meaning into the verb itself.

English uses a phrasal verb: write down.
Russian uses a single verb: записать.

So записать already includes the idea of to write down / note down, and you do not need an extra word for down.

Here его means his.

It modifies имя, so the phrase его имя means his name.

Russian его can mean either:

• his as a possessive
• him in some case forms of он

In this sentence, it is clearly possessive because it comes right before a noun:

• его имя = his name

A useful thing to remember: possessive его does not change form. Unlike мой, твой, and many other pronouns, его stays его.

It is in the accusative case here, but for this noun the accusative singular looks the same as the nominative singular.

• nominative: имя = name
• accusative: имя

That is normal for many inanimate nouns in Russian. Since имя is the direct object of записал, it is accusative, but the form happens to stay имя.

Because Russian uses different cases after в depending on the meaning:

• в + accusative = movement into / direction into
• в + prepositional = location inside

Here, the idea is that the name was written into the notebook, so Russian uses в блокнот.

Compare:

• Я записал его имя в блокнот. = I wrote his name down in/into a notebook.
• Его имя уже есть в блокноте. = His name is already in the notebook.

So:

• в блокнот = destination
• в блокноте = location

Записал is perfective, so it presents the action as a completed whole: the speaker finished writing the name down.

That fits English I wrote down his name very well.

Compare:

• записал = wrote down, completed
• записывал = was writing down / used to write down / wrote down repeatedly
• писал = was writing / wrote, but without the specific write down sense

So this sentence focuses on a single completed result: the name got written into the notebook.

Yes, this is a natural, neutral word order.

Russian word order is flexible, but changing it usually changes emphasis rather than basic meaning.

For example:

• Я записал его имя в блокнот. = neutral
• Его имя я записал в блокнот. = emphasizes his name
• В блокнот я записал его имя. = emphasizes into the notebook

So the original sentence is a good standard version.

Yes, very often.

Russian past tense verbs show gender and number, so записал already tells you:

• past tense
• singular
• male speaker

Because of that, if the subject is clear from context, Russian can simply say:

• Записал его имя в блокнот.

That is completely normal in conversation.

The main stresses are:

• Я записАл егО Имя в блокнОт.

A few pronunciation notes:

• записал is stressed on the last а
• его is stressed on the last о
• имя is stressed on the first syllable
• блокнот is stressed on the last syllable

Also, его is often pronounced more like йиво than exactly as it is spelled. That is very common in normal speech.

Usually, записал is better here.

• записал = wrote down, noted
• написал = wrote, composed, produced in writing

So:

• Я записал его имя в блокнот = I wrote down his name in a notebook.
• Я написал его имя = I wrote his name.

The second one is possible in some contexts, but it does not emphasize the idea of noting it down the way записал does.