UPDATE this post apply for Exchange Online 2010; for Exchange Online 2013 see http://blog.hametbenoit.info/Lists/Posts/Post.aspx?ID=486
On Office 365, all user with an Exchange account has an email address hosted at onmicrosoft.com (firstname.lastname@example.org).
Here is a step by step to add an alias to a user (using the something.onmicrosoft.com suffix or your own internet domain name).
This has not to be done if you have enabled Directory Synchronization with Office 365.
If you have your own internet domain name and want to use it, you have to add it on Office 365 first (follow these steps http://blog.hametbenoit.info/Lists/Posts/Post.aspx?ID=236).
So, logon to Office 365 administration portal with an account with administrative rights (https://portal.microsoftonline.com/)
Then click on the Outlook click shown at the top.
This will open your Outlook mailbox through Outlook Web Access.
Then, open the Options and go to Set all options
From the Options menu, open Manage My Organization
You are now on the Users & Groups page, select the user you want to assign an alias and click on Details
Open the E-Mail Options section and click to the Add button
Enter the alias you want to add and select the domain to use; if you have added your internet domain name successfully on Office 365, you will see it on the drop down list