Yes! The earliest evidence of hull-name removal is this photo, Hibiki (Akatsuki-class) in Dec 1941:
Anyway, from the photo of Ayanami and Shikinami in my last post, it can be inferred that the Hiragana (not Katakana on the side) names astern were always remain.
As for larger ships such as CLs and CAs, they've never been painted Katakanas on their side-hull.