Typically, most of these services are uniform—i.e. include the same tools and features (send a script, they record it in a tone you approve, they send it as a file, you supply any feedback, etc.); however, there are some services that go above and beyond. For example, VoiceOverPro, is a single voice professional who records 30 second voicemail messages based on users’ scripts. This is standard; however, users also have options like adding music, recording up to 60 seconds (or 150 words), rush, 2-day turnaround, and even same day delivery.
Hello! Thanks for calling [LinkedPhone’s Customer Success Team]. We are currently helping other customers achieve their goals and want to do the same for you! Please leave a message with your name, number, and a brief description of how we can serve you. We promise to return your call [before close of business today]. In the interim, you can also check out our website at [linkedphone.com] for helpful answers to our most common requests. Thank you.

Finally, you can mention your name in the recording. This is a good idea if your calls are still coming into a cell phone. If you’re on a first name basis with all your customers, it adds that extra personal touch to include your name in the voicemail. If you’re not on a first name basis, but you’d like to be, then use your name to encourage customers to use it!
You should acknowledge that right off the bat by apologizing that they couldn't reach you directly.