Asegúrate de escribir bien tu apellido en el formulario.

Because the verb here is asegurarse de, which means to make sure.

• asegurar = to assure / to insure / to secure, depending on context
• asegurarse de = to make sure of something

This sentence is giving a command to you in the informal singular (tú) form, so:

• asegura = assure / insure / secure
• asegúrate = make sure

The te is part of the reflexive verb asegurarse.

Because asegurarse normally goes with de + infinitive when it means to make sure to do something.

So the pattern is:

• asegurarse de + infinitive

Examples:

• Asegúrate de llamar. = Make sure to call.
• Asegúrate de traer el documento. = Make sure to bring the document.

So in your sentence:

• Asegúrate de escribir... = Make sure to write...

Because after de, Spanish uses the infinitive when the subject stays the same.

Here, the person who must make sure and the person who must write are both you, so Spanish uses:

• Asegúrate de escribir...

Compare:

• Asegúrate de escribir bien tu apellido. = Make sure to write your surname correctly.

If the subject changed, Spanish would usually use que + subjunctive instead:

• Asegúrate de que él escriba bien su apellido. = Make sure that he writes his surname correctly.

It is informal singular: a command to tú.

So this sentence is talking to one person in an informal way.

Other versions:

• Formal singular (usted): Asegúrese de escribir bien su apellido en el formulario.
• Informal plural in Spain (vosotros): Aseguraos de escribir bien vuestro apellido en el formulario.
• Formal plural (ustedes): Asegúrense de escribir bien su apellido en el formulario.

Since you are learning Spanish from Spain, the vosotros version is especially useful.

The accent is needed because a pronoun has been attached to the imperative form.

Start with:

• asegura (the tú affirmative command)

Then add the reflexive pronoun:

• te

That gives:

• asegurate

But Spanish spelling rules require the stress to stay in the correct place, so it becomes:

• asegúrate

The accent mark shows that the stress stays on gú.

Here bien means something like properly, correctly, or clearly enough to avoid mistakes.

So escribir bien tu apellido means:

• to write your surname correctly
• to make sure it is spelled properly

It does not just mean nicely in a handwriting sense, although in some contexts it could include writing clearly.

Yes, you could say:

• Asegúrate de escribir correctamente tu apellido en el formulario.

This is grammatically correct, but bien sounds more natural and everyday in many situations.

So:

• bien = more common, natural, conversational
• correctamente = more formal or explicit

• nombre = first name / given name
• apellido = surname / last name

Examples:

• Me llamo Laura. Laura es mi nombre.
• García es mi apellido.

In forms, you may also see:

• nombre
• apellidos (often plural in Spanish, because many Spanish-speaking people use two surnames)

So tu apellido here means your surname/last name.

Because the sentence is addressing you informally (tú), so the possessive is tu.

• tu apellido = your surname (informal singular)
• su apellido = his/her/your surname (formal singular or other meanings depending on context)

If the command were formal, it would be:

• Asegúrese de escribir bien su apellido en el formulario.

En el formulario means on/in the form.

Spanish often uses en where English might say on with documents, forms, or pages.

So:

• en el formulario = on the form / in the form

This is the normal preposition here.

Yes, a little. The original sentence is the most natural neutral order:

• Asegúrate de escribir bien tu apellido en el formulario.

You could also hear:

• Asegúrate de escribir tu apellido bien en el formulario.

But this is usually less smooth. Keeping bien right after escribir is very natural because it clearly modifies the action of writing.

So for learners, the safest pattern is:

• Asegúrate de escribir bien + thing

Usually it mainly suggests spelling it correctly, especially in the context of a form.

However, depending on context, it can also imply:

• write it clearly
• don’t make mistakes
• fill it in properly

If you wanted to focus specifically on spelling, Spanish could say:

• Asegúrate de escribir correctamente tu apellido...
• Asegúrate de no escribir mal tu apellido...

But the original sentence is natural and broad.

A natural version would be:

• Asegúrate de no escribir mal tu apellido en el formulario.

Notice that no goes before the infinitive:

• de no escribir

You could also say:

• No escribas mal tu apellido en el formulario. = Don’t write your surname incorrectly on the form.

But that is a direct negative command, not exactly make sure.