Learn Hardcore German: Neben dem Straßennamen schreibe ich zusätzlich die Hausnummer. - Next to the street name I also write the house number.

Because neben is a two-way preposition. With a static relation (where something is/exists “beside”), it takes the dative: neben dem …. With a directional relation (movement/placement “to a position beside”), it takes the accusative: neben den ….

Static: Der Stuhl steht neben dem Tisch. (dative)
Directional: Ich stelle den Stuhl neben den Tisch. (accusative)

In your sentence the phrase means “besides/in addition to the street name,” which is a static/relational use, so dative is used: neben dem Straßennamen.

Why does Straßenname become Straßennamen here?

Because Name is a so‑called weak noun (n‑declension). Its oblique cases (all but nominative singular) add -n/-en:

Nom. sg.: der Straßenname
Gen. sg.: des Straßennamens
Dat. sg.: dem Straßennamen
Akk. sg.: den Straßennamen

So with dative after neben, you get dem Straßennamen.

Is Straßennamen here singular or plural?

Singular (dative). The article dem shows it’s masculine dative singular. Plural would be die Straßennamen (nom./acc.), and dative plural would be den Straßennamen (with article den and the noun already ending in -n).

Could I say neben den Straßennamen instead?

Yes, but it changes the meaning to directional/placement: Ich schreibe die Hausnummer neben den Straßennamen = “I write the house number (to a position) next to the street name.” Note this form is string-identical with the dative plural (neben den Straßennamen), so the article alone may not disambiguate; context normally does.

Is zusätzlich redundant with Neben dem …?

A bit. Neben … already implies “in addition to.” Zusätzlich emphasizes that idea. Grammatically it’s fine; stylistically you can drop one:

Neben dem Straßennamen schreibe ich die Hausnummer.
Zusätzlich zum Straßennamen schreibe ich die Hausnummer.
Ich schreibe neben dem Straßennamen auch die Hausnummer.

Where can I put zusätzlich?

Typical placements:

Midfield (neutral): … schreibe ich zusätzlich die Hausnummer.
Fronted for emphasis: Zusätzlich schreibe ich …
After the object (less common): … schreibe ich die Hausnummer zusätzlich. All are correct; German prefers adverbs before the direct object.

Why is the verb before ich?

German main clauses are verb‑second (V2). The first “slot” is taken by Neben dem Straßennamen, so the finite verb schreibe must come second, and the subject ich follows: [Neben dem …] [schreibe] [ich] …

Why die Hausnummer and not der Hausnummer?

Hausnummer is feminine. As a direct object it’s in the accusative, but feminine nominative and accusative are both die:

Nom./Acc. sg.: die Hausnummer
Dat. sg.: der Hausnummer Here it’s the thing being written, so accusative: die Hausnummer.

Should it be eine Hausnummer instead of die Hausnummer?

Use die if it’s the specific house number belonging with that street name (the usual case in an address). Use eine if you mean “a house number (one of possibly many, not specific).”

What’s the difference between zusätzlich, außerdem, and auch?

zusätzlich = additionally, in addition (adverb modifying the action): Ich schreibe zusätzlich …
außerdem = moreover/besides (sentence adverb; adds a new point): Außerdem schreibe ich …
auch = also/too (focus-sensitive; often directly before what’s added): Ich schreibe auch die Hausnummer. All can work, but they differ in nuance and placement.

Can I say zusätzlich zu instead of neben?

Yes: Zusätzlich zum Straßennamen schreibe ich die Hausnummer. Here zum = zu dem (dative). This avoids the potential directional reading of neben and is very natural.

Does außer dem Straßennamen mean the same as neben dem Straßennamen?

No. außer is typically exclusive: “except for/apart from.”
Außer dem Straßennamen schreibe ich die Hausnummer is likely understood as “I don’t write the street name; I (only) write the house number.” Use neben or zusätzlich zu for “besides/in addition to.”

Why is Straßenname written as one word? What’s the extra -n?

German compounds are written as one word: Straße + Name → Straßenname. The -n- is a linking element (Fugen-n), common in compounds. Then the head noun Name declines: Straßennamen (dat./acc. sg., etc.).

Do I need a comma after the fronted prepositional phrase?

No. Neben dem Straßennamen is not a clause; German does not use a comma here.

Does the present tense schreibe mean a habitual action or can it refer to the future?

Both are possible. German present can express:

Habitual/general: “I (usually) write…”
Scheduled/near future with context: “I’ll write…”
Context decides; as-is, it most naturally reads as habitual.

How is ß in Straßennamen spelled elsewhere? Is ss correct?

In Germany/Austria you write Straße/Straßenname with ß. In Switzerland/Liechtenstein you write Strasse/Strassenname with ss. Both follow their regional standards.

Pronunciation tips for Straßennamen and Hausnummer?

Straßennamen: long “a” in Straße; ß = voiceless “s”; double n across the compound boundary: [SHTRAH-sen-NAH-men].
Hausnummer: diphthong “au” like “house”; stress on the first syllable: [HOWSS-noo-mer].

Can I move the prepositional phrase to the end?

Yes, but the case can shift with meaning:

Placement (directional): Ich schreibe die Hausnummer neben den Straßennamen. (accusative)
Relational/“in addition to”: keep the dative and meaning clear by fronting or using zu: Neben dem Straßennamen schreibe ich die Hausnummer. / Ich schreibe die Hausnummer zusätzlich zum Straßennamen.

Can I drop ich?

No. German is not a pro‑drop language. You must state the subject pronoun: ich schreibe ….