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Clients will be a lot less likely to leave a message if they wonder who will get it. Use a warm friendly voice to say something like, “You have reached xxxx, licensed mental health counselor.”

You should acknowledge that right off the bat by apologizing that they couldn't reach you directly.
The simple truth is that you need to be more aware of what you’re leaving for other people to hear. Sure, this doesn’t always register as a priority for users, but it’s never too late to reassess your greeting. a. Reading/Speaking in the Imperfect Tone: Tone is absolutely everything. Users don’t want to come off as being too nice, as it sounds insincere, or being too terse, as it can be interpreted as being rude. That being said, striking the right balance is absolutely essential. Your greeting exists as its own entity, and therefore, it should NOT rely on callers’ familiarity with you. Instead, it needs to appeal to the masses. As such, your inflection, i.e. the way you state your name and directions, needs to be both welcoming and firm. b. Injecting Humor & Insincerity: While humor/light heartedness can be welcoming, it can also convey a sense of informality, insincerity, and ultimately unprofessionalism. Why, because you’re not there to lend your humor or to contextualize. Instead, you’re assuming the caller has a working knowledge of your personality to ground the message. Though this might not sound like it’s all that terrible—it can be detrimental. As stated above, one should NEVER rely on a caller’s familiarity with you. Instead, aim to appeal to the masses. Humor is ultimately subjective, meaning not everyone has the same tastes; therefore, someone is bound to be turned off by a quirky or off-color remark. While implementing a light-hearted or even tongue and cheek tone can work, it’s just a really bad idea.