I only saw one therapist who used a service to answer calls (the first one I ever saw about 30 years ago and answering machines were not yet everywhere and certainly no voicemail etc)- and the service clearly identified themselves. And why wouldn't therapist just tell the client that they used a service. I checked with the one I see now who gives out her home number to make sure no one else would get her messages. I would not blindly trust a therapist.