Yes, you can allow callback requests without displaying your phone number in the Zendesk Web Widget.
To achieve this, go to the Admin Center, access Talk settings, and select the Widget tab. Under Contact options, choose 'Request a callback' from the drop-down menu. This setting will hide your phone number while still enabling customers to request a callback from your support team.
To hide your phone number in the Zendesk Web Widget (Classic), you have two options. If you want to keep the option for customers to request a callback, navigate to Admin Center, go to Talk settings, select the Widget tab, and under Contact…
Disabling Talk in the Zendesk Web Widget is straightforward. To do this, go to the Admin Center, navigate to the Web Widget page, and select the Customization tab. Here, you will find a slider for Talk. Simply toggle this slider to the off position…