Je dois écrire mon nom sur le formulaire.

Because the verb is devoir, and dois is the je form in the present tense.

Present tense of devoir:

• je dois
• tu dois
• il / elle / on doit
• nous devons
• vous devez
• ils / elles doivent

So with je, you must say je dois.

It can mean either I must or I have to.

In this sentence, je dois expresses obligation or necessity. In natural English, I have to write my name on the form is often the most everyday translation, while I must write my name on the form can sound a little stronger or more formal.

Because after devoir, the next verb stays in the infinitive.

The pattern is:

subject + devoir + infinitive

So:

• Je dois écrire
• Tu dois partir
• Nous devons attendre

This works a lot like English:

• I must write
• You must leave
• We have to wait

Because nom is a masculine singular noun, so the correct possessive adjective is mon.

French possessive adjectives must agree with the thing being possessed, not with the owner.

So:

• mon nom = my name
• mon livre = my book
• ma voiture = my car

Even if the speaker is female, she would still say mon nom, because nom is masculine.

Because in French, a possessive adjective usually replaces the article.

So French says:

• mon nom
• ton adresse
• sa signature

Not:

• le mon nom
• la ton adresse

This is different from English, where articles and possessives also do not normally go together, so the idea is actually similar once you notice it.

Because sur is the normal way to say on in this context.

So:

• sur le formulaire = on the form
• sur la feuille = on the sheet
• sur le document = on the document

Using dans le formulaire would usually sound less natural here. Dans means in/inside, and although English sometimes says in the form, French commonly uses sur for writing something on a document.

Le formulaire usually refers to a specific form that is already known from the situation.

For example, if someone hands you a form and says what you need to do, French often uses le:

• Je dois écrire mon nom sur le formulaire.

If you were talking about any form in a general sense, un formulaire could be possible:

• Je dois remplir un formulaire.

So le here suggests the form in question.

Yes, it is the most neutral and standard word order.

The structure is:

Je + dois + écrire + mon nom + sur le formulaire

That is:

• subject
• conjugated verb
• infinitive
• direct object
• prepositional phrase

French word order is often less flexible than English, so this is a very natural basic sentence.

You probably could be understood, but it sounds less natural as a basic sentence.

The most normal order is: Je dois écrire mon nom sur le formulaire.

Putting sur le formulaire before mon nom can sound marked or awkward unless there is a special reason to emphasize where you must write it.

It is pronounced roughly like ay-kreer, but with French sounds.

A few points:

• é sounds like a clear ay
• cri sounds like kree
• the r is the French r, not the English one

So écrire is approximately ay-kreer, but the exact French pronunciation is more precise than that rough English guide.

A rough English-style guide would be:

zhuh dwah ay-kreer mohn nohn syur luh for-myoo-lair

A few useful details:

• Je often sounds like zhuh
• dois sounds like dwah
• nom has a nasal vowel, so it is not exactly like English nome
• sur does not sound exactly like English sir
• formulaire ends with a French r sound

This kind of guide is only approximate, but it can help you get started.

It depends on context.

In everyday language, nom can simply mean name in general. But on official forms, French often distinguishes:

• nom = surname / family name
• prénom = first name / given name

So in a real administrative context, mon nom might sometimes be understood specifically as a last name, depending on the form.

Sometimes, yes, but écrire is the simplest and safest choice.

• écrire = to write
• inscrire = to write down, enter, register, or fill in formally

Inscrire can sound a little more formal or administrative. For a beginner, Je dois écrire mon nom sur le formulaire is an excellent, natural sentence.

They are similar, but not identical.

• Je dois écrire mon nom = I have to / must write my name
• Il faut que j’écrive mon nom = It is necessary that I write my name

The second structure is more advanced because it uses que plus the subjunctive: j’écrive. For learners, je dois + infinitive is usually the simpler pattern to start with.