"With an e-vote, how do you make sure whatever the voter decided is what got into the storing database without, at the same time, losing the voter's anonymity?"
A one-way hash function serving as a checksum for the ballot content combined with the voter identity.
If a person wants to verify that their vote is in the database, they go to a web cafe and enter the hash function that is on their vote receipt and the db reports that it has a ballot-answer-set with that hash.
If this is concerning, because someone might force the person to submit their hash at a specific time and have a collaborator on the inside look at which ballot that is so determine how the person voted, there is another variant of this hash-based verification where all that can be verified is that the vote, as cast, was in fact part of the count. If enough percent of randomly selected voters verify that their vote was counted, via the hash method, the election can statistically be considered sound.
I think Chaum's system includes this capability.