I don't know about you, but when i vote, my name is not printed on the ballot anywhere.
It's one of the reasons electronic elections (internet based) are hard to do and audit properly. It's not like an ATM, where you identify the person, and the account and can keep the books auditing the transactions. Once the vote is cast, it is anonymous. Guaranteeing anonymity while at the same time, validating that the individual is a legitimate voter is harder to do electronically than you think. Done right, it involves cryptographic blinding protocols.
In the copy of the Democratic voters who voted twice, there is an i.d. number/barcode listed beside each name. One would think the ballot they were handed had the same barcode. You wouldn’t need a name if you could match a ballot number to a name.