Are your user accounts synced with AD to O365 (DirSync / FIM), or are the user accounts hosted on O365 itself?
If the user accounts are hosted in an internal AD and synced, then any of the methods for allowing users to update their own internal info are still applicable. The changes will just sync during the regular DirSync / FIM update. The way Snowknight26 posted should work (it used to, bur I haven't done it since XP).....But there are free Web based utilities that provide nice interfaces too (run on a local IIS server)....