It is the "treason of the clerks" in her comments that is offensive (and not just offensive to immigrants). She wants the the culture to bend - and everyone to fill out some forms - just to make her life easier. Go screw.
Three of the four contributors here don't use their legal first names in normal life. Out of Jack, Bob, Ted, and Pete only Pete comes close (he's a Peter); the rest of can't even spell our AKAs using all the letters in first/middle/last as scrabble tiles (not even Bob, who has about 57 letters in his first/middle/last).
Nicknames generate very little friction in practice, and even then the small frictions only occur when dealing with treasonous clerks (as opposed to plain clerks). The United States Bowling Congress doesn't give a rat's ass that Jack isn't my given name; it happily keeps track of my league average regardless. United Airlines does care (or rather clueless TSA clerks do); I occasionally get hassled when a ticket says "Jack" instead of "John" on my ID.
The legislator's singling out of immigrants is especially hilarious. The apocryphal stories of Ellis Island clerks American-izing last names is exactly wrong. Immigrants (and especially Asians) Americanize their names. I grew up with a Willy Chung. His given name was Willy, not William, because his parents wanted to name him something super American. The kicker? They did know some "William"s but thought they were named "Willy" because that's what they went by in normal life!
Screw the clerks. Every time you hear a legislator talk about "creating efficiencies" instead hear that they want you to change your behavior and your culture. Just to make their jobs a little easier.