Departments and teams are typically organized by function – customer service, tech support, sales, billing questions, etc. When a team is busy handling other calls, encourage your callers to leave a message and reassure them that you will get back to them within a reasonable time frame. It’s important that you actually follow through to avoid upsetting your callers.
Last but not least a slogan or branding: this is really more important for new customers and people that are calling or leaving a voicemail for the first time rather than returning ones (though it helps a little with them too!). A catchy phrase makes it easier for people to remember your name and recognize you when you give them a call back.

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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!