Pišem svoje ime.

In Serbian, the verb ending often already tells you who the subject is.
Pišem means I write / I am writing, so ja is not necessary.

You can say Ja pišem svoje ime, but that usually adds emphasis, such as:

• Ja pišem svoje ime, a on svoje. = I am writing my name, and he is writing his.

So in a neutral sentence, leaving out ja is completely normal.

Pišem is the 1st person singular present tense of pisati = to write.

So it can mean:

• I write
• I am writing

In Serbian, the present tense often covers both the simple present and the present continuous meanings that English separates.

The -m ending marks 1st person singular in the present tense for this verb.

So:

• pišem = I write
• pišeš = you write
• piše = he/she/it writes

That final -m is one of the clues that makes the subject pronoun unnecessary.

Svoje is the reflexive possessive pronoun, from svoj, and Serbian normally uses it when the owner is the same as the subject of the sentence.

Here, the subject is I and the name also belongs to that same person, so:

• Pišem svoje ime = I am writing my own name

This is the most natural choice.

Moje ime can mean my name, but in a sentence like this, moje is less natural unless you are stressing contrast, for example:

• Pišem moje ime, ne tvoje. = I’m writing my name, not yours.

Because svoj has to agree with the noun it describes.

The noun ime is:

• neuter
• singular

So the matching form is svoje.

Compare:

• svoj brat = one’s own brother
• svoja knjiga = one’s own book
• svoje ime = one’s own name

The possessive adjective changes form to match the noun, not the person who owns it.

Here ime is in the accusative singular because it is the direct object of pišem.

You are writing what?
ime

A useful detail: for many neuter nouns in Serbian, the nominative and accusative singular look the same. So:

• nominative: ime
• accusative: ime

That is why the form does not visibly change here.

A rough English-friendly pronunciation is:

PEE-shem SVO-yeh EE-meh

A few key sounds:

• š sounds like sh in ship
• j sounds like y in yes
• every vowel is clearly pronounced

So:

• Pišem ≈ PEE-shem
• svoje ≈ SVO-yeh
• ime ≈ EE-meh

Yes, absolutely.

Both are correct:

• Pišem svoje ime.
• Ja pišem svoje ime.

The version without ja is more neutral and more typical in everyday Serbian.
The version with ja adds emphasis, contrast, or clarity.

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

The neutral order here is:

• Pišem svoje ime.

But other orders are possible for emphasis:

• Svoje ime pišem. = It is my name that I’m writing.
• Ime svoje pišem. = more literary or marked

So the original sentence is the most natural everyday version, but Serbian can move words around to change focus.

Because pisati is imperfective, and it describes the action as ongoing, repeated, or simply in progress.

So:

• Pišem svoje ime. = I am writing my name / I write my name

The verb napisati is perfective and focuses on completion. It is used when the action is seen as finished or completed, for example:

• Napisao sam svoje ime. = I wrote / have written my name

So for a plain present action in progress, pišem is the right choice.

Yes. Serbian can be written in both Latin and Cyrillic scripts.

The Cyrillic version is:

Пишем своје име.

Letter by letter:

• Pišem → Пишем
• svoje → своје
• ime → име

Both scripts are standard in Serbian.