Your Microsoft tenant name is part of your domain name with regards to Microsoft Office 365 Services. You can identify your tenant name accessing the OneDrive Pro app or the like via the web and checking the text that’s written in the address bar of your browser. Your address bar will look something like this:
When you sign up for Office 365, you are asked for your organization name (i.e., mydomain). Based on that name, Microsoft will allocate a “tenant name” for you, so you are given an initial SharePoint domain which looks like mydomain.sharepoint.com.
Note that even if you add a new domain to be used with your Office 365, you can’t rename “tenant name”. For example, if you chose fourthcoffee as your organization name during Office 365 signup, then fourthcoffee will become your “tenant name.” Even if you add domain fabrikam.com, you cannot change your SharePoint domain to be fabrikam.sharepoint.com.