You are free to do whatever you want with the source code. The images depicting Ubuntu and Canonical are copyrighted and have to be removed (that includes images in packages itself). Those should all be marked with a (c).
You are even allowed to use the Ubuntu repositories to fetch your release.
But if it is given to organizations under a separate name (saying it is a derivative of ubuntu), does this not require permission from Ubuntu or Canonical?
No, but you are not allowed to leave an impression that you are related to Canonical or Ubuntu and/or that this release is in any way related to Ubuntu. You are also not allowed to mimick the name Ubuntu. Claiming a derivative of Ubuntu without also expressing it is unofficial might raise eyebrowses (I am not a lawyer but that to me might cross a border).
Your system most likely will NOT be officially endorsed. The Ubuntu derivatives that are there now cover each a large audience either by language (chinese) or a specific desktop evironment (kde, lxde) each with their own niche (feature-rich, or mainly about supporting older hardware and speed).
To become an official member of the Ubuntu family you need approval from the members of the Ubuntu Technical Board.
The Ubuntu Technical Board is responsible for the technical direction that Ubuntu takes. The Technical Board makes final decisions over package selection, packaging policy, installation system and process, toolchain, kernel, X server, library versions and dependencies, and any other matter which requires technical supervision in Ubuntu.
Ubuntu MATE seems to become the newest member in the Ubuntu family.