- First one is by using the following web page: http://o365.rocks/. There you will be able to do a quick check for the availability of a tenant name in Office 365.
- The other approach is just to use the PowerShell script you can find here: https://www.linkedin.com/pulse/how-check-office-365-tenant-name-availability-aaron-dinnage
Screenshots and original post here: https://jcgonzalezmartin.wordpress.com/2016/11/21/office-365-how-to-know-if-a-tenant-name-is-available-or-taken/