Good question. The Caller ID display of the person you call can show different messages. If you are using the Yahoo! Phone Out service, the word "Anonymous" or "Unavailable" is shown in the Caller ID of the person you're calling.
If you use the Yahoo! Phone In service, and have one Yahoo! Phone In, the default setting will be that number, not "Anonymous." If you have more than one Yahoo! Phone In, the default setting will be the last number purchased.
If you're using the Yahoo! Phone In service, you can choose "Anonymous" (or any of the numbers you have purchased). To set the Caller ID preference: