In Japan the same kanji 鯛 is read 'tai,' a classic auspicious fish served at celebrations (the wordplay 'medetai' = 'congratulations'). Common Chinese compounds: 真鲷 (red sea bream), 黑鲷 (black porgy), 鲷鱼烧 (taiyaki, fish-shaped pastry).
Fish radical on the left, the indexing component. Pictograph of a fish: head on top, scaled body in the middle, tail-fin below. Almost every left-fish char names a species - 鲤 carp, 鲨 shark, 鲸 whale, 鳕 cod - and 鲷 'sea bream' fits the pattern.
Right side 周 zhōu supplies the sound with a regular initial shift zhōu to diāo (an old retroflex alternation). Same phonetic appears in 调 tune/diào, 雕 carve/diāo, 凋 wither/diāo - all sharing the diao reading.