You can only do it if your domain isn't private :(
Keep in mind that major providers such as Gmail, Outlook.com and Yahoo will look sideways at any email traffic coming from private domains, as these are often a major source of spam!
This is why we only allow you to authenticate your domain and add our CNAME if you've got public WHOIS records. In case you don't know how to switch them from private to public, just ask the folks in charge of your domain hosting to do it for you.
We understand you may not want to disclose your personal contact info out to the world, but private domains will not only damage your deliverability but you even risk losing domain ownership! Some domain extensions can help you protect your info - if privacy is key, consider going for one of these.