Blog - Using a custom domain name for your SharePoint Online public website address

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When you create a public website on SharePoint Online, as an administrator, you can set up the site to use a custom domain name instead of using the domain name that you chose when you signed up for Microsoft Office 365 for enterprises, for example,contoso.sharepoint.com. This helps customers find your website by using the more familiar domain name that you bought for your business.

To use a custom domain name with Office 365, do the following. Read Blog: http://www.dshift.com/blog/using-a-custom-domain-name-for-your-sharepoint-online-public-website-address/