The plan is not coherent. Some items to consider:

Who is verifying the documents? If the names have to match, what about people who change their names? What documents should they present to prove that that's their real name? How will the election worker actually verify that the documents are correct?

Women who have changed their names after getting married have a higher burden of proof than people that have not changed their name. The folks who wrote this act are aware of this.

The SAVE Act, in particular, puts in place criminal and civil penalties for election workers that fail to properly identify someone. But a random election worker is not equipped to make that judgment perfectly and is going to end up making mistakes, since document verification for things like birth certificates is completely manual.

Young voters are more likely to have the documents like a birth certificate back at their parents' house and they're not likely to yet have a passport. Likewise, poorer voters do not have the resources to easily obtain these documents. Passport costs over $100 in the United States and for someone that doesn't travel often is not a very good investment. Just because you can't afford an expensive government document does not mean you're not entitled to your vote.

If Silicon Valley has taught me anything, it's every time you add friction to a process, fewer people have the resources and/or are willing to go through it as they drop off the funnel. In this case, it's targeted at the young, the poor, and the women. We used to be a nation that would say: get out and vote! Participate in our democracy! Now we're looking for excuses to not let citizens vote if they can't prove on the spot that they're a citizen. Papers, please.

And all that for what? Multiple institutions, including the Cato Institute and the U.S. Department of Justice, have found no evidence of meaningful voter fraud. This is because identification is required during voter registration, which is effective in preventing illegal immigrants from voting. This is why we tie voter registration to things like getting a driver's license at the DMV. You already have all your documents prepared that you gathered for that visit, and so that's the right time to be checking all of them.