I due nomi rimano.

Because nomi is a masculine plural noun, and it begins with a normal consonant sound (n).

For masculine plural nouns, Italian uses:

• i before most consonants: i nomi, i libri
• gli before vowels and certain consonant clusters: gli amici, gli studenti, gli zaini

So i nomi is correct.

Both are possible, but they do not mean exactly the same thing.

• i due nomi = the two names
• due nomi = two names

The article i makes the phrase definite: we are talking about two specific names already known from the context.

That is the normal order in Italian when you have a definite article plus a number:

• i due nomi
• le tre case
• i quattro ragazzi

So the structure is:

article + number + noun

This often feels a little different from English, but it is standard Italian.

No. Due does not change.

It stays due with both masculine and feminine nouns:

• i due nomi
• le due ragazze
• i due libri
• le due case

So unlike many adjectives, due has the same form in all these cases.

Yes. The singular is nome and the plural is nomi.

This can look a little surprising, because many -e nouns form the plural in -i, but nome is especially worth remembering because it is a very common word:

• il nome = the name
• i nomi = the names

Rimano is the third-person plural present tense of rimare.

So:

• rima = it rhymes
• rimano = they rhyme

Since the subject is i due nomi (the two names), the verb must also be plural:

• Il nome rima.
• I nomi rimano.

Yes, rimare exists and is correct. However, Italian also very commonly uses fare rima.

So you may see both:

• I due nomi rimano.
• I due nomi fanno rima.

Both mean that the two names rhyme. Depending on context, fare rima can sound especially natural in everyday Italian.

I due nomi rimano is the most neutral, standard order.

Italian word order is more flexible than English, so other orders are possible for emphasis, for example:

• Rimano i due nomi.

But that sounds more marked or stylistic. For a learner, I due nomi rimano is the safest and most natural basic version.

A simple guide is:

ee DOO-eh NOH-mee REE-mah-noh

A few helpful points:

• i = ee
• due has two syllables: du-e
• nomi = NOH-mee
• rimano = REE-mah-noh

So do not pronounce due like one English syllable; in Italian it is normally du-e.

Usually nomi means names. In some grammar-related contexts, nome can also be used in a broader grammatical sense, but for noun, modern Italian more commonly uses sostantivo.

So in a normal sentence like this, a learner should understand nomi as names unless the context clearly says otherwise.

Because Italian usually does not need subject pronouns when the subject is already clear.

Here the subject is explicitly stated as i due nomi, so adding a pronoun would be unnecessary.

Italian commonly says:

• I due nomi rimano.

not:

• I due nomi loro rimano.

The noun phrase itself is enough.