I'm affraid it is not possible - at least not without investigating possibilities of EF Designer extensibility or investigating EdmGen internals. The point of Entity designer is to allow you easily map / change those names.
Interestingly it is possible if you start with model (EF designer) and want to generate database from the model - in such case the process is controlled by workflow and T4 templates and you can change it but in case of generating model from database the process is most probably hardcoded inside Edmgen tool - you can check if this tool has any API which would allow you changing the behavior.
Anyway EDMX is just XML so if you have exact pattern you need to replace you can create very simple tool, transformation or script which will modify your EDMX file after generation from the database.
You cannot change the POCO T4 template. The template must produce classes with exactly same names as you have for entities in your model. Otherwise the POCO magic will not work.