The story
Pseudo-loan from Danish. The name was coined by the creator of the brand, who intended it to seem Danish to honour Denmark for aiding Jews during the Holocaust, but to be unique. The words have no meaning and Danish does not actually use the letter ä or the digraph zs. The Hong Kong pronunciation is influenced by Cantonese 哈根大師 /哈根大师 (haa¹ gan¹ daai⁶ si¹).
Etymology from Wiktionary, CC BY-SA 4.0.