Если Вы не уверены, проверьте фамилию и отчество в анкете ещё раз.

Capitalized Вы is a polite, respectful way to write you in Russian, especially in instructions, letters, forms, and official communication.

A few important points:

• Вы = formal singular you or plural you
• вы with a lowercase letter is also grammatically correct in many contexts
• Capitalizing it adds politeness and formality

So in this sentence, Вы shows that the speaker is addressing the reader respectfully, not casually.

Because уверены here is the short form of the adjective уверенный.

Russian often uses short-form adjectives after words like я, ты, вы, мы to express a state or condition:

• Я уверен = I am sure
• Она уверена = She is sure
• Вы уверены = You are sure

So Если Вы не уверены literally means If you are not sure.

Why not неуверенный?

• неуверенный is usually a full adjective meaning something like unsure, insecure, lacking confidence, and it normally describes a noun:
  • неуверенный человек = an insecure / uncertain person
• In this sentence, Russian wants the short-form predicate:
  • Вы не уверены = You are not sure

The ending matches the person being described.

Short-form adjective endings are:

• masculine singular: уверен
• feminine singular: уверена
• neuter singular: уверено
• plural: уверены

Since Вы can be either:

• plural you, or
• formal singular you

Russian uses the plural form with Вы, so it becomes уверены.

That is why you say:

• Ты не уверен
• Вы не уверены

Проверьте is the imperative form of проверить, meaning check / verify.

More specifically, it is:

• the command form
• plural or formal

Compare:

• проверь = check! (to one person informally)
• проверьте = check! (to several people or to one person formally)

Since the sentence uses polite Вы, the command also takes the polite/plural ending -те.

So:

• Если ты не уверен, проверь...
• Если Вы не уверены, проверьте...

Because фамилию is in the accusative case.

The verb проверить takes a direct object: you check something. That direct object goes into the accusative.

• nominative: фамилия
• accusative: фамилию

So:

• проверить фамилию = to check the surname

This is normal for feminine nouns ending in -я:

• анкета → анкету
• фамилия → фамилию

Because отчество is also the direct object of проверьте, but for this noun the accusative looks the same as the nominative.

Отчество is a neuter inanimate noun, and neuter inanimate nouns usually have:

• nominative: отчество
• accusative: отчество

So in the sentence:

• проверьте фамилию и отчество

both nouns are objects of check, but only фамилия visibly changes form.

Отчество is a patronymic: a name based on a person’s father’s first name.

It is an important part of the traditional full Russian name system:

• имя = first name
• отчество = patronymic
• фамилия = surname / last name

For example:

• Иван Сергеевич Петров
  • Иван = first name
  • Сергеевич = patronymic
  • Петров = surname

A native English speaker may not have an exact equivalent in English, which is why this word often stands out.

Because в here means in / on the form, and after в when talking about location, Russian uses the prepositional case.

• анкета = form, questionnaire, application form
• prepositional singular: в анкете

So:

• в анкете = in the form / on the form

English often says on the form, but Russian naturally says in the form with в.

Ещё раз means again or more literally one more time.

• ещё = still / more / another
• раз = time, occasion

So:

• проверьте ... ещё раз = check ... again / check ... one more time

This is a very common Russian expression.

Examples:

• Скажите ещё раз = Say it again
• Прочитайте ещё раз = Read it once more

Because the sentence begins with an if-clause:

• Если Вы не уверены, ...

In Russian, subordinate clauses introduced by words like если are normally separated by a comma.

So the structure is:

• Если
  • clause, main clause

This is very similar to English:

• If you are not sure, check...

Because Russian usually does not use a subject pronoun with the imperative unless it is needed for emphasis.

So Russian naturally says:

• Проверьте фамилию... = Check the surname...

not usually:

• Вы проверьте фамилию...

Adding Вы would sound more emphatic, contrastive, or stylistically marked in many contexts.

In other words, the verb form проверьте already tells you that this is a polite/plural command, so the pronoun is unnecessary.

Yes. In an informal situation, you would normally switch both the pronoun and the verb forms.

Formal/polite:

• Если Вы не уверены, проверьте фамилию и отчество в анкете ещё раз.

Informal singular:

• Если ты не уверен, проверь фамилию и отчество в анкете ещё раз.

If speaking to a woman informally:

• Если ты не уверена, проверь фамилию и отчество в анкете ещё раз.

So several forms change:

• Вы → ты
• уверены → уверен / уверена
• проверьте → проверь

Yes, in most contexts фамилия means surname / last name / family name.

A learner should just remember that Russian official forms often ask for:

• фамилия = surname
• имя = first name
• отчество = patronymic

So if you see фамилия и отчество, the form is asking you to check your surname and your patronymic specifically.