Now I have a spellcaster on level 7 in all 4 areas (Conjurer, Magician, Sorcerer, Wizard) !
I read everywhere that he is now an Archmage. But how does he become it ?

She is still called "Conjurer". The review board does not offer any class change to Archmage.
I understand that Archmage spells are only introduced in the Destiny Knight.
But how do I get at least the title Archmage in BT 1?

Archmage in bt1 is just having all magical classes having learned all spell levels
there was no indicator of this status sadly, not until BT2 whee it became an actual class

so in other words, if you have learned all spells from each magical class you are an Archmage
and have to pretend you have a fancy title and outfit


sad, but there it is. the ugly truth of the BT 1 Archmage