On Session, you can edit your display name to whatever you'd like—just remember that this is how your name will display in all groups and communities.
Mobile (iOS and Android):
To change your Session display name, click on your profile icon in the top left corner of the app to open Settings. Then, simply click on your display name, edit and save.
Desktop:
To change your Session display name, click on your profile icon in the top left corner of the app. Then, click on the pencil icon next to your display name in the pop-up to edit and save.