Google Voice allows you to change your standard voicemail greeting in its Settings section, and Google also lets you create a custom greeting for a group or for an individual. You set up your greeting through the Google Voice website, though you will need access to one of the phones you have registered to Google Voice.
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At the Google Voice website, click the gear icon and select "Settings" and then click "Voicemail & Text." If you already have multiple greetings recorded, select the one you want to change in the drop-down menu beside "Voicemail Greeting" and click "Re-record"; if you only have one greeting already recorded, simply click "Re-record." If you have more than one phone associated with Google Voice, select it from the drop-down menu that appears and then click "Connect." Your phone will ring, and when you answer you will be prompted to record your greeting. After you hang up, the Google Voice website will then prompt you to save your new greeting.
To record a custom greeting for a group, click "Groups & Circles" in Settings and then click "Edit" beside the group you want a custom greeting for. To record a custom greeting for an individual, click the History section of Google Voice and then click that person's name. In either case, you can now click "Re-record," select the phone you want Google to call and then click "Connect" to receive a call and record a new custom greeting. After hanging up you must save the greeting when asked at the Google Voice site.