Actually I got that from the AKB0048 manga that just started serialization.
The 1st chapter has the Kenkyusei refer to some of regular members with names of real life AKB member and it explains that top members will get carry on the name of legendary members based on their style and resemblance.
The keys here is that there are multiple of them so clearly the generational designation isn't some that they shares among them but unique to each name. And like I said inhering names is a fairly common practice in skill professions in East Asia, especially in Japan.
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