How to create a Distribution List in Office 365
First login to the Office 365 Admin Center:
Find the Admin-->Exchange shortcut on the navigation pane on the left side, scrolling down you will find it near the bottom of the list (pictured above).
This will take you to a new window, opening the "Exchange Admin Center".
By default you will load to the dashboard, so select "Recipients" below the dashboard; and Groups from the above menu (pictured below).
Now select the drop down arrow next to the + symbol, and select "Distribution group" (pictured below).
*Please note the option to select Security groups and Dynamic distribution groups, both useful for managing group permissions or managing a list by user details field (not explained in this article).
After you create the new Distribution Group, you will now need to fill out some information (pictured below):
*Display name : Type in the name you want to be displayed when receiving an email from this address.