To log in to the Office365.com site, users will use their OU e-mail address. If a user has set an e-mail alias in the past, they will use this for their username. An e-mail alias is an alternate version of your email address which will still send mail to your same mailbox.
Because e-mail aliases can be updated, ones login username will also change to reflect this update. Please note that there is a two day update cycle for the Office 365 username field. This means that it will take the system two days to update to your new alias as the username. So until the system updates, you may have to continue to use your previous alias for your username.
For example, if you have email@example.com set as your alias, you will use that as your username. If you change your alias from firstname.lastname@example.org to email@example.com on a Monday, then it might not be until Wednesday that firstname.lastname@example.org is recognized as your new username. Until that time, you would need to continue to use email@example.com as your username.