I'm a newbie on AI myself and surprised that the AI team did not realise that a Developer might need to change a screen name on-the-fly, it's not an issue in other languages :). However, it's fair to say that there is no such thing as a perfect programming language, nor a perfect IDE. The AI concept is brilliant, AI2 a sturdy implementation of that concept.
So, one half-way solution would be for each Student to add a Screen to their Individual Project, giving it the name required for the Collaborative Project. The blocks can be copied from 'Screen 1' to the Back Pack and from the Back Pack to the 'New Screen'. 'Screen 1' could then be deleted*, but if the Student has defined a GUI (Designer) for her/his contribution, it looks like that will have to be redone (take a screenshot of the GUI layout first and work from there).
Hopefully, one of the experienced AI Users knows of a far better way, but if the individual projects are small then not much time will be lost.
*Edit: I see that AI2 allows you to delete any screen except Screen1 - it sounds as though the name Screen1 is a dependency:
Could it be that the Merger App is "Screen1" aware, and you just have to ensure the project names are unique? Looking at the documentation, I think it is: