That's fine, if no one else wants to contest. The child won't be able to tell Lea her name - she's just too far gone by that point. However, as Lea's leaving with the others while the cavern collapses behind him, he'll hear that same, cryptic voice in his mind. FLIT. The voice doesn't clarify, but Lea will know without a doubt that it's the child's name.

Completely up to you guys how you choose to have the argument play out.