A measure of similarity? Then I demand all people sounding like me to license their voice from me.
A claim that the voice originates from a certain person? Then you don't need any licensing in this case.
I'm not sure. Precedented personality rights would be a good place to start [1].
I'd argue for a higher standard of evidence for human-produced voices, Middler v. Ford Motor Co. seems good as any [2]. But a lower burden for synthesised voices, given the difficulty in proving intent and mass producibility of them.
> A claim that the voice originates from a certain person? Then you don't need any licensing in this case
Altman basically claimed as much by tweeting about Her in its context. At that point, he is using her fame to market his products without her permission.