Learn German: Er nennt diese schnelle Bewegung einen Angriff. - He calls this fast movement an attack.

The verb nennen (to call or to name) is one of the few German verbs that take a double accusative. The first accusative is the thing being named (diese schnelle Bewegung), and the second is the name or title you are giving it (einen Angriff).

Why is it einen Angriff instead of ein Angriff?

Angriff is a masculine noun (der Angriff). Even though it might feel like it just describes the movement (like a predicate noun after the verb 'to be'), it is still an accusative object required by the verb nennen. Therefore, the article ein must take the masculine accusative ending and become einen.

How do I know which of the two accusative objects is the main object and which is the name?

Just like in English, the thing being named usually comes first, followed by what it is called. Here, he is naming the movement (Bewegung) an attack (Angriff). The standard word order makes this clear.

Why does the adjective schnelle end in -e here?

Bewegung is a feminine noun, and it follows the demonstrative pronoun diese, which acts like a definite article. For feminine nouns in the accusative case after a definite article, the adjective takes the weak ending -e.