Drifting into cybersecurity, the fundamental flaw is that a person's name a poor identifier because it is not unique. This was recognized at the dawn of data-processing, when "account numbers" were created.
In @CraginS's case, the bank would be much better served by verifying that the two accounts have a common SSN. They have legitimate right to that particular piece of PII and using it for purposes of account merging seems reasonable, given that the need to validate the tax-reporting implications.
In @Thembalethu's case, (ISC)²/PersonVue's goal of ensuring the same ID is used both for registration and examination would be better served by leveraging a piece of unique data, such as the License/ID number.
And when it comes to national election security, signatures make a very poor authenticator for that same reasons that names are a poor identifier. Signatures are not consistent over time, are relatively easily forged, and (as Craig said), require a trained eye to validate.
The cybersecurity relevant part of the Voter-ID movement is that it basically strives to change authentication from "something you know" (how to form your signature) to "something you have" (your ID card).
