Da die Gruppe neu ist, schreibt jede Person ihren Namen auf ein Namensschild.

Da has more than one use in German.

Here, da is a conjunction meaning since or because:

• Da die Gruppe neu ist, ... = Since/Because the group is new, ...

In other contexts, da can also mean there:

• Er ist da. = He is there / He is here.

So the meaning depends on the sentence structure. In your sentence, da introduces a clause with its own verb, so it means because/since, not there.

Because da introduces a subordinate clause. In German subordinate clauses, the conjugated verb usually goes to the end.

So:

• die Gruppe ist neu → normal main clause
• da die Gruppe neu ist → subordinate clause, so ist moves to the end

This is a very common pattern with words like:

• weil = because
• dass = that
• wenn = if/when
• obwohl = although
• da = since/because

German uses a comma to separate a subordinate clause from the main clause.

So the structure is:

• Da die Gruppe neu ist, = subordinate clause
• schreibt jede Person ihren Namen auf ein Namensschild. = main clause

This comma is required in standard German.

This is because German main clauses follow the verb-second rule.

When the sentence begins with the subordinate clause Da die Gruppe neu ist, that whole clause takes the first position. The conjugated verb of the main clause must then come immediately after it.

So the pattern is:

• [First position], [verb] [subject] ...
• Da die Gruppe neu ist, schreibt jede Person ...

If you started directly with the subject, you would say:

• Jede Person schreibt ihren Namen auf ein Namensschild.

But once the da-clause comes first, schreibt must come before jede Person.

Because jede Person means each person, and jede is singular.

So the subject is grammatically singular:

• jede Person = each person
• therefore: schreibt = singular verb form

Compare:

• Jede Person schreibt. = Each person writes.
• Alle Personen schreiben. = All people write.

Even though the meaning refers to multiple people in the group, German treats jede Person as singular.

Ihren is a possessive determiner here, meaning her in a grammatical sense, but in English the natural translation may be their because of each person.

There are two things happening:

1. Person is a feminine noun in German: die Person
2. Name is masculine: der Name

Because the possessor is jede Person, German uses the ihr- form.
Because Namen is masculine and in the accusative, the form becomes ihren.

So:

• base idea: ihr Name = her name
• accusative masculine: ihren Namen

Even if Person refers to people of any gender, the noun Person is grammatically feminine, and that affects the possessive form here.

Because the noun being referred back to is die Person, and Person is grammatically feminine.

So German uses:

• jede Person ... ihren Namen

not

• jede Person ... seinen Namen

Even if in English you might think of each person as gender-neutral, German is following the grammatical gender of Person.

A learner-friendly way to think about it is:

• Person = feminine noun
• so the possessive linked to it is ihr-

Because Name is one of the masculine nouns that change in certain cases. It belongs to a group often called weak nouns or n-nouns.

The basic form is:

• der Name = the name

But in the accusative, dative, and genitive singular, it usually adds -n or -en:

• nominative: der Name
• accusative: den Namen
• dative: dem Namen
• genitive: des Namens

So in your sentence, ihren Namen is the correct accusative form.

Because auf is a two-way preposition, and here German uses the accusative to show the idea of writing something onto the surface of the name tag.

So:

• auf ein Namensschild schreiben = write onto a name tag
• auf einem Namensschild stehen = be written on a name tag / be located on a name tag

A helpful contrast:

• Sie schreibt ihren Namen auf ein Namensschild.
  She writes her name onto a name tag.

• Ihr Name steht auf einem Namensschild.
  Her name is on a name tag.

In the first sentence, the writing is being placed onto the tag, so accusative is natural.

Namensschild is a compound noun:

• Name = name
• Schild = sign, label, badge

Together, Namensschild means name tag / name badge / label with a name on it.

The -s- in the middle is a common linking element in German compounds. It does not always have a separate meaning; it just helps connect the parts:

• Name
  • Schild → Namensschild

German has many compounds like this, and learners often just need to memorize them as vocabulary items.

Yes, in many situations you could.

• Da die Gruppe neu ist, schreibt jede Person ihren Namen auf ein Namensschild.
• Weil die Gruppe neu ist, schreibt jede Person ihren Namen auf ein Namensschild.

Both can mean because the group is new...

But there is a slight difference in feel:

• da often sounds a bit more formal or written
• da often introduces a reason that is treated as known or obvious background information
• weil is very common in everyday speech

So da works especially well here because it sounds like background explanation.

Because all nouns are capitalized in German.

So in this sentence:

• die Gruppe
• jede Person
• ihren Namen
• ein Namensschild

are all capitalized because they are nouns.

This is one of the most noticeable spelling differences between German and English.

The sentence has two parts:

1. Da die Gruppe neu ist
   = subordinate clause giving the reason

2. schreibt jede Person ihren Namen auf ein Namensschild
   = main clause

A useful breakdown is:

• Da = since/because
• die Gruppe = the group
• neu = new
• ist = is
• schreibt = writes
• jede Person = each person
• ihren Namen = her/their name
• auf ein Namensschild = onto a name tag

So grammatically, it is:

• Reason clause + main clause

This is a very common and useful German sentence pattern.