JHM is right about the reason. John Fultz shows nice versioning and coding style I'm encouraging to use but it doesn't answer how to avoid this problem in general and flexible way.

Here is my attempt, I will skip JF enhancement to not complicate things. The problem is that whatever symbol name we use it may happen that the collision will occur with something somewhere. The solution is then to ensure that the context in which `update` is parsed will be unique.

We can achieve this sticking to two rules:

- each "modular" gui element  should be defined in own "subcontext"

 So e.g. between ``Begin["`inner`"]/End[]``

- DynamicModule variables should be typed with a backtick `` `update`` so that we are sure that even when `update` is somewhere in `$ContexPath` "our" `update` will be `` `inner`update``.

Here is a minimal example of such package:


    ClearAll["GUI`*"];
    BeginPackage["GUI`"];
    
      inner; outer;
      update (*it isn't part of the solution, it is here to simulate \
               "update" being on context path*)
    
    Begin["`Private`"];
    
    
    
    Begin["`inner`"];
    
      inner[Dynamic[x_, args___]] := 
        DynamicModule[{`update}, Print@{"inner:", SymbolName@`update};
          `update[] := (Print@"inner"; args@1);
          Slider[Dynamic[x, (`update[]; x = #) &]]];
    
    End[];


    
    Begin["`outer`"];
    
      outer[Dynamic[x_, args___]] := 
        DynamicModule[{`update}, Print@{"outer:", SymbolName@`update};
         `update[] := (Print@"outer"; args@1);
         {inner[Dynamic[x, (`update[]; x = #) &]], Dynamic@x}];
    
    End[];
    
    End[];
    
    EndPackage[];

Now, since we have ``GUI`Private`inner`update`` and ``GUI`Private`outer`update`` there is no collision. Which was achieved with minimal effort and works even when ``GUI`update`` is always on `$Path`.


    x = 1;
    outer[Dynamic@x]

Prints `inner/outer`