I voted maybe ~ I'd use aliases, and it would depend on a lot of factors, namely the public outlet (some, well imo most programs are out for sensationalism and even those that may have a genuine interest in telling the truth present the possibility of things getting twisted around by another source looking to discredit not only a child's (or adult's) memories but reincarnation in general; it seems that's how some folks/organizations operate, the beliefs they hold can't stand on their own, so they opt to try to tear down other belief systems and individuals who think differently than they do.
That said, I love reading about the memories and experiences others have, so I do appreciate their being brave (and generous!) enough to share their (and their children's) memories and the process they went through in remembering.