Я не могу вспомнить его имя.

Russian often uses a modal-style construction here:

• могу = I can / am able to
• вспомнить = to recall / to remember

So Я не могу вспомнить его имя literally means I cannot recall his name.

This is very similar to English I can't remember his name, except Russian expresses it as I can't + recall.

This is one of the most important things to notice in the sentence.

• помнить = to remember, in the sense of having something in your memory
• вспомнить = to remember / recall, in the sense of bringing it back to mind

So:

• Я помню его имя = I remember his name
  (I know it; it is in my memory.)
• Я не могу вспомнить его имя = I can't remember his name
  (I can't bring it to mind right now.)

In this sentence, вспомнить is the natural choice because the speaker is trying to recall something.

Because it follows могу.

After мочь (to be able / can), Russian normally uses the infinitive of the main action:

• Я могу прийти = I can come
• Я могу помочь = I can help
• Я не могу вспомнить = I can't remember / recall

So могу is the conjugated verb, and вспомнить stays in the infinitive.

Here его means his.

That can be confusing, because его can also mean him, depending on the sentence.

In его имя:

• его = his
• имя = name

So the phrase means his name.

Russian possessive words like его and её do not change for case, gender, or number in the same way many adjectives do:

• его имя = his name
• его книга = his book
• его друзья = his friends

So here, think of его simply as the possessive his.

In this sentence, имя is in the accusative case, because it is the direct object of вспомнить.

However, имя is a neuter noun, and for inanimate nouns like this, the accusative is often the same as the nominative.

So:

• nominative: имя
• accusative: имя

That is why the form does not visibly change here.

In Russian, не with verbs is usually written separately:

• не знаю = I don't know
• не хочу = I don't want
• не могу = I can't

So не могу is the normal spelling.

Yes, absolutely.

• Я не помню его имя = I don't remember his name
• Я не могу вспомнить его имя = I can't remember his name

These are close in meaning, but there is a slight nuance:

• не помню sounds like I don't remember
• не могу вспомнить sounds like I can't recall it right now, often with a sense of trying and failing

In many real situations, both are natural.

Yes, Russian often drops subject pronouns when they are clear from the verb form.

So you can say either:

• Я не могу вспомнить его имя
• Не могу вспомнить его имя

Both mean I can't remember his name.

The full version with я may sound a bit more explicit or emphatic, but both are normal.

Yes. Russian word order is more flexible than English word order.

The neutral order here is:

• Я не могу вспомнить его имя.

But you may also hear:

• Его имя я не могу вспомнить.
• Я его имя не могу вспомнить.

These variations can shift emphasis:

• Его имя я не могу вспомнить emphasizes his name
• Я его имя не могу вспомнить may emphasize contrast or what exactly cannot be recalled

For learners, the original sentence is the safest and most neutral version.

Yes, вспомнить is perfective.

Russian verb aspect matters a lot:

• вспоминать = imperfective, to be recalling / trying to remember
• вспомнить = perfective, to recall successfully / bring to mind

In не могу вспомнить, the perfective is natural because the idea is I can't manage to recall it.

Compare:

• Я пытаюсь вспомнить его имя = I’m trying to remember his name
• Я не могу вспомнить его имя = I can't remember his name
• Я вспоминаю его имя is less natural in this exact meaning and usually suggests the ongoing process of recollection

So the perfective infinitive is the standard choice here.

A simple pronunciation guide:

• Я = ya
• не = nye
• могу = ma-GOO
• вспомнить = fspOM-neet'
• его = yi-VO
• имя = EE-mya

Approximate full pronunciation:

ya nye ma-GOO fspOM-neet' yi-VO EE-mya

A couple of useful notes:

• его is spelled with г but pronounced like в: yevo / yivo
• вспомнить begins with a consonant cluster that can feel difficult at first

The stressed syllables are:

• Я
• не
• могу́
• вспо́мнить
• его́
• и́мя

So:

Я не могу́ вспо́мнить егó и́мя.

Stress is very important in Russian, because it is not always predictable. It is worth memorizing stress together with the word.

Yes, in some contexts его can also mean its, because Russian does not have a separate possessive word for its in the same way English does.

So его имя could theoretically mean:

• his name
• its name

But in ordinary conversation, context usually makes it clear. In this sentence, learners usually understand it as his name.