https://en.wikipedia.org/wiki/Midler_v._Ford_Motor_Co.
"The appellate court ruled that the voice of someone famous as a singer is distinctive to their person and image and therefore, as a part of their identity, it is unlawful to imitate their voice without express consent and approval. The appellate court reversed the district courts decision and ruled in favor of Midler, indicating her voice was protected against unauthorized use.[4][5]"
I was actually a little surprised. And this is different, but I think that they're imitating a famous voice (as opposed to my voice...) means they become a target.
The fact you can fake anyone saying anything is little amazing. though there are people who can do it quite well:
https://en.wikipedia.org/wiki/Josh_Robert_Thompson
Thompson's Arnold Schwarzenegger impression first gained national attention during the California gubernatorial recall election of 2003. Posing as Schwarzenegger, Thompson phoned in to Fox News Channel's morning program, Fox & Friends, fooling the hosts into believing (at least for a short while) that he was, in fact, Schwarzenegger.[4]