Session Account usernames (also called ONS) are permanent names that can be purchased and assigned to an Account ID. Once assigned, other people can contact you using your username instead of your Account ID. People still have the option of contacting you using your Account ID if they prefer. One Account ID can have multiple usernames assigned to them.
To learn more about Session usernames and how to purchase one, you can visit this page.
Display names are the names you choose for yourself in Session when you create an Account ID. This is how your name will appear to other people on their contacts screen. You can also change the display name of your existing contacts in your conversation settings screen. Display names can be changed at any time, but you can’t use a display name to add a contact on Session.