I’ve been trying to build a collection of screens for use in different presentations or multiple use within one presentation. The problem I’m having is in managing the encapsulation of these collections so that they can be slotted in with minimal effort.
Update: Sorry, this posting was wrong so I’ve deleted most of it. See later posting.
If I’m understanding this correctly, I believe this already happens. In the past, you needed unique component names. This isn’t necessary anymore as long as you aren’t grabbing information from other screens. I don’t remember exactly when this change happened, but it’s fairly new. So basically, you should be able to copy and paste your second screen without it breaking. 
Thanks @cwinske and apologies everyone! Single screens are indeed fine. I’m working with multiple screens but tried to explain the problem with a simpler example. Here is another simplified case that hopefully makes the point properly this time!
In this example, the first screen can be used on its own to capture a single value, using definitions entered through a table. The next two screens form a pair, where the first captures a value and the second draws a graph based on an aggregate of those values or uses a dummy table if the class is not running.
In using the second pair, name clashes are reported and need to be resolved (as shown). I suppose what I’m suggesting is having some way to extend the local scope currently available for one screen across two or more .
Apologies for the initial confusion.
A step forward in building collections of useful screens is to have a label on each screen. It appears that facility is already in Desmos but its use is restricted:
Is there a problem in making this facility more widely available?
Those aren’t custom labels like you may think. They’re used to separate predefined segments in our curriculum activities.
Sorry, my misunderstanding…but I’d still like to see custom labels for screens. 