I do think it was blown out of proportion, but as an elected official, you DO need to watch what you say or how you say it, especially on the public record.
I know exactly what she is talking about though, and I have had to deal with it myself as an IT administrator.
For example my Korean friend Jae Kim. But he goes by David. I said, "If you want to Americanize your name, why not just go by Jay?"
He said that "David" is actually the name that his parents gave him when the family moved to America when he was an infant. David really is his name given by his parents, not just something he adopted himself. His birth certificate and passport shows Jae.
His driver's license reads David.
I can see how this can cause problems for things like voter registration and/or checking in at polling places.
There are TONS of people who work here in this office that have one name for a login, one name for email, and a nickname that you address them with.
I think if she is having trouble with Asian names in Texas, her head would explode in Hawaii.