Я не помню название этого фильма.

Помнить means to remember or to have in memory, while знать means to know.

So:

• Я не помню название этого фильма = I don’t remember the title of this film
• Я не знаю название этого фильма would mean I don’t know the title of this film

In English, I don’t remember and I don’t know can sometimes feel similar, but in Russian they are usually kept distinct.

Название is the direct object of помню, so it goes in the accusative case.

However, название is a neuter inanimate noun, and for neuter inanimate nouns, the accusative form is identical to the nominative.

So:

• nominative: название
• accusative: название

That is why the word does not visibly change.

Because this part means of this film.

The phrase название этого фильма literally means:

• название = title / name
• этого фильма = of this film

In Russian, possession or of relationships are often shown with the genitive case.

So:

• фильм = film
• этого фильма = of this film

And the adjective/pronoun этот changes too:

• masculine nominative: этот
• masculine genitive: этого

That is why both words change.

Yes, you can.

Both of these are possible:

• Я не помню название этого фильма
• Я не помню названия этого фильма

The first uses the accusative object form. The second uses the genitive, which can appear after negation in Russian.

In modern everyday Russian, Я не помню название этого фильма is very common and natural. Я не помню названия этого фильма is also correct, and may sound a bit more bookish, formal, or stylistically marked depending on context.

For a learner, the accusative version is a very good standard choice.

Russian has no articles like a or the.

English says:

• the title
• this film

Russian expresses definiteness through context, word order, and words like этот (this).

So название этого фильма naturally means the title of this film even though there is no separate word for the.

Yes, Я can often be omitted in Russian, because the verb ending already shows the subject.

• помню = I remember

So both are possible:

• Я не помню название этого фильма
• Не помню название этого фильма

The version with Я is slightly more explicit and can sound more natural when the subject is being emphasized or when the sentence stands alone. The version without Я is also very common in conversation.

Yes, Russian word order is flexible.

This order is the most neutral and straightforward:

• Я = subject
• не помню = verb phrase
• название этого фильма = object

But other orders are possible for emphasis, for example:

• Название этого фильма я не помню = The title of this film, I don’t remember
• Этого фильма название я не помню = possible, but more marked and less neutral

Russian often changes word order to shift focus, emphasis, or contrast.

Не is the standard particle for negation, meaning not.

It usually goes directly before the verb:

• помню = I remember
• не помню = I do not remember

So:

• Я помню название этого фильма = I remember the title of this film
• Я не помню название этого фильма = I do not remember the title of this film

Here are the dictionary forms:

• Я → я = I
• не → не = not
• помню → помнить = to remember
• название → название = title, name
• этого → from этот = this
• фильма → фильм = film, movie

So the sentence is built from very common vocabulary and a very common grammar pattern.

Usually either one works.

Russian фильм can mean:

• film
• movie

In everyday English, movie is often the most natural translation in many contexts. But if the provided meaning uses film, that is also perfectly fine.

So:

• Я не помню название этого фильма
  can be understood as
  I don’t remember the title of this movie/film.

Because of meaning and case.

The sentence means the title of this film, so этого belongs with фильма.

Also, their forms match:

• этого = masculine/neuter genitive singular
• фильма = masculine genitive singular

Meanwhile, название is neuter singular accusative here, so этого is not describing название.

If this were modifying название, you would expect something like:

• это название = this title

But that is not what this sentence says.

No. Название is a general word meaning name or title for things such as:

• books
• films
• songs
• articles
• companies
• places

Examples:

• название книги = the title of the book
• название песни = the title of the song
• название компании = the name of the company

So in this sentence it specifically means title, because we are talking about a film.