Þetta fornafn er auðvelt að muna.

Because fornafn is a neuter noun, and the demonstrative has to agree with it.

The Icelandic word for this changes for gender and case:

• þessi = masculine/feminine nominative singular
• þetta = neuter nominative singular

So:

• þetta fornafn = this pronoun
• not þessi fornafn

Agreement is very important in Icelandic, much more than in English.

Fornafn is neuter.

You often just have to learn a noun’s gender with the word, but here there is also a helpful clue: the second part, nafn (name), is a neuter noun, and compounds built on it are often neuter too.

So when you learn fornafn, it is best to remember it as:

• fornafn — a neuter noun

That is why the sentence uses:

• þetta fornafn
• auðvelt

both in neuter singular form.

Because it agrees with the subject þetta fornafn, which is neuter singular.

The adjective auðveldur means easy, but its form changes by gender:

• auðveldur = masculine
• auðveld = feminine
• auðvelt = neuter

Since fornafn is neuter, Icelandic uses:

• Þetta fornafn er auðvelt

So the -t ending is not random; it shows neuter singular agreement.

Að muna is the infinitive, meaning to remember.

The word að is the usual infinitive marker, similar to English to in many situations.

So:

• muna = remember
• að muna = to remember

In this sentence, að muna goes with auðvelt:

• auðvelt að muna = easy to remember

This is a very common pattern in Icelandic:

• er erfitt að skilja = is hard to understand
• er gott að lesa = is good to read
• er auðvelt að muna = is easy to remember

This is the same kind of structure as English This pronoun is easy to remember.

Even though this pronoun is the thing you remember, it is still the grammatical subject of the whole sentence:

• Þetta fornafn = subject
• er = is
• auðvelt = easy
• að muna = to remember

So the sentence works like an English easy-to-remember construction. You do not need an extra object after muna, because it is already understood from the subject.

You can think of it as:

• This pronoun is easy [for someone] to remember.

In this sentence, it is nominative, because it is the subject of er.

However, there is a useful detail: for many neuter words, nominative and accusative look the same. So the form þetta fornafn could also appear as an object elsewhere without changing shape.

Compare:

• Þetta fornafn er auðvelt að muna.
  Here it is the subject, so nominative.

• Það er auðvelt að muna þetta fornafn.
  Here it is the object of muna.

The form looks the same, but the grammatical role is different.

Yes. That is also a natural Icelandic sentence.

It means essentially the same thing, but the structure is different:

• Þetta fornafn er auðvelt að muna.
  Focuses first on this pronoun.

• Það er auðvelt að muna þetta fornafn.
  Starts with it is easy to remember..., more like a general statement.

So both are possible. The version you were given is useful because it shows a very common Icelandic pattern where the noun being described comes first.

Because þetta already gives the meaning this pronoun.

In Icelandic, you normally do not combine a demonstrative like þetta with the suffixed definite article in the way English uses this plus the.

So:

• fornafn = pronoun
• fornafnið = the pronoun
• þetta fornafn = this pronoun

That is why plain fornafn is correct after þetta.

Yes, absolutely. It is a very useful pattern.

You can use it with many adjectives:

• Þessi bók er auðveld að lesa. = This book is easy to read.
• Þetta orð er erfitt að bera fram. = This word is hard to pronounce.
• Þessi regla er góð að kunna. = This rule is good to know.

So the model is:

• [noun phrase] + er + adjective + að + infinitive

In your sentence:

• Þetta fornafn
  • er
    • auðvelt
      • að muna

Learning this pattern will help you build many natural Icelandic sentences.