I would argue that for most US-citizen minors on domestic trips, there is simply no way for the TSA to conclusively verify their name. There's no requirement for the kid or the parents to carry any ID or custody papers, and most little kids won't have enough public records (or a credit report, or voter registration records with political affiliation) to go through TSA's alternate ID verification procedure. If TSA is linking up with Social Security or the IRS (which could do verification in most cases, since parents are now extorted into getting their kids SSNs at birth), then that should be a major news story.

The worst that could happen is a TSO asking the kid his name (I've heard of them doing that and may have even seen it once or twice). But if you book the trip under the kid's middle name, or nickname, or simply spelled-differently real name (Cathy vs Kathi, Steven vs. Stephen, etc.), that's not going to be an issue.

I think booking the kid under "George Bush" or "Mickey Mouse" would be a bad idea (unless one of the parents' last name is Bush or Mouse). But substantial variations on their real name that an adult couldn't get away with under Secure Flight make perfect sense.