I would like to check the file name, and see if it already exists elsewhere in the media tree? (Requirement from our client)

It will currently prompt that file is there is same folder, but I need to extend this to entire tree.

What event should I subscribe too for catch when a new media item is uploaded?
I am hoping I can hook into that event, then scan Media tree, and see if it's a duplicate (I'm aware there will probably be a overhead here, and will feed this back to client) 

Thanks
Danny