Learn Icelandic: Ég nefni þig formann.

The verb nefna (to name or appoint) is a double accusative verb. This means it takes two objects that must both be in the accusative case: the person being named (þig) and the title or role they are being given (formann).

I know the dictionary form for chairman is formaður. Why does it change to formann?

Compound words ending in -maður (man or person) follow an irregular declension pattern. In the accusative singular, the ending becomes -mann. Therefore, the accusative form of formaður is formann.

If I change this to the passive voice to say 'You are named chairman', do the words stay in the accusative?

No, they switch to the nominative case. When a double accusative verb is used in the passive voice, it becomes a double nominative construction. The sentence would become Þú ert nefndur formaður.

Could I use the verb kalla instead of nefna for this sentence?

Grammatically yes, because kalla is also a double accusative verb. However, the meaning changes slightly. Nefna is used for formally appointing someone to a role or position, whereas kalla generally means to refer to someone by a specific name or nickname.