But Mira is pronounced meera surely, so a different name from Myra? I don't see the problem, it's nice.
I imagine that if there was no such person as Myra Hindley, Myra itself would be a popular name right now, as it seems to fit right in with Mila, Maya etc that are currently fashionable. Will the MH association ever go away? People didn't stop calling boys Ian did they? (Although not currently popular).