Currently it's not possible to edit and update your profile information directly from Outlook for iOS, but it is possible to edit this information elsewhere.
To make updates to your profile go to:
Outlook for Windows File/Office Account/User information/About me (brings you to Office 365 profile online)/Update Profile or click on the camera icon to change your photo).
Or go to Outlook on the Web (OWA) Profile image/My profile/ Update profile.
