Looks like it's now canon that KANSEN named after their predecessors inherit their appearance and personality.
It's not inheritance; they're the exact same character, just with different rigging (the devs even say their skins will be interchangable). Canon seems to imply that a KAN-SEN is the embodiment of every ship with that name. Zuikaku talks about CV-2 and CV-16 Lexington as if they were the same person; if you sortie the two together Zui says something like "One victory for each of us, ready to fight again?". In Rondo at Rainbow's End, when Elizabeth meets Friedrich, her reaction is not "Who are you?" but "You look different from the last time I saw you," referring to the Kaiser-class Friedrich der Große from WWI.
