Thanks for calling Dial-A-Shrink. I can’t come to the phone right now, so after the tone, please leave your name and number, then talk briefly about your childhood and tell me what comes to mind when you hear the following words: orange… mother… unicorn… penis. I’ll get back to you with my diagnosis as soon as possible.
We weren't even allowed to do that, in case family members (or whoever) found out that an NHS person had called. Clearly policies do differ somewhat, and it sounds like you have a more useful compromise ;-)

That’s why it’s critical that each customer interaction with your business is consistent, positive, and represents the values and personality of your company. This includes your storefront, website, social media presence, emails, and every interaction you have with your customers, both online and in-person.
Once you finish your voicemail message, you can end on a note of gratitude and express thanks or that you realize the recipient of the message us busy, so you’d appreciate a return call. Whichever way you choose, make certain that the tone of your message is upbeat. A business voicemail greeting sees each call as their chance to engage with their clients or vendors. Hello, you’ve reached the office of Lydecker and Lydecker. We are currently unavailable to answer your call. However, your call is important to us, so please leave your name, phone number or email address, and a brief message and we’ll get back to you as soon as possible. Thank you for your interest in Lydecker and Lydecker Law Offices. Professional tone Provide the caller with specific information Request the caller to leave specific information Extend gratitude for their call Professional Voicemail Greetings