If you've installed RealActualBankApp (with the ID of real.actual.bank.app) once (from whatever source!) then there cannot be another app installed with that same id but signed with a different public key (oversimplified version of the story, there is a key rollover scheme).
You can however install an imposter app that's also called RealActualBankApp, with the same icon. It'll need to go by a different ID.
So then we're down to the same problem, or pseudo-problem, of identity confusion, as we have for banking website URLs. Where is the ID/URL shown, and does the user know that it should be mybank.com and not mybank-incorporated.com ?