You can identify yourself with only your first name on a personal cell phone or home voice mail. If it is a business voicemail, I suggest including your first and last name. I would also include your title.
A professional voicemail greeting is a recorded message that welcomes callers to your business when no one is available to pick up the call. For a polished call experience, the greeting should reflect who the client is calling – whether a general business number, department, team, or individual – and when the customer can expect the call to be returned.

In the Phone app , Visual Voicemail (available from select carriers) shows a list of your messages. You can choose which ones to play and delete without listening to all of them. A badge on the Voicemail icon indicates the number of unheard messages.
Recording your professional voicemail greeting can sometimes cause apprehension, especially if you have never done so before. You may find it helpful to go to a very private location when you are ready to record, and this can help ensure there is no background noise when you are finished. Take a few minutes to review the list you made earlier, and rehearse the greeting a few times if you are extremely nervous. While you are rehearsing, make sure your speech flows smoothly and you do not use filler words like "uh" or "um". Is Amazon actually giving you the best price? This little known plugin reveals the answer. Professional voicemail greetings should be pleasant in tone to encourage customers to call back later.