Having Returning Anonymous Function Access Global Function

Use a function expression instead of function declaration.
So your code will look like this

_myGlobalFunct = function(str) {}

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See : https://javascriptweblog.wordpress.com/2010/07/06/function-declarations-vs-function-expressions/

greetings 894359, , I looked at what you call an "anonymous function" as -

return (function() {
  var rvalue = document.title || "No Title";
 window._myGlobalFunct(rvalue);
return rvalue;
})();


To me, the problem is when you placed the "return" as the FIRST operation in that progression, I can not see as there is Anything to return "TO", so I can not understand Why you even placed the "return" there at the beginning? ? and you have your "anonymous function" returning a String, Why? ? if you do not use that string on the return, why have a string return?

I have tried this in firefox and it works -

var r = "";

r = (function() { 
  var rvalue = document.title || "No Title";
 _myGlobalFunct(rvalue+"!!");
return rvalue+"!!";
})();

document.title = r;

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Please notice that I have a return variable as -
      r =
for the function, so it can use the result of the text change,
ALSO I have NOT used the     window.      in-
       window._myGlobalFunct(rvalue);

and have it as a more practical -
       _myGlobalFunct(rvalue+"!!");
whay place a     window.     if it's not needed ?

One last observation, I do not see as using this "anonymous function" is any coding or functional advantage, so why use it?
couldn't you just use -

var rvalue = (document.title || "No Title")+"!!";
 _myGlobalFunct(rvalue);
document.title = rvalue

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Just a little clarification, these are NOT the exact functions I'm using,  so don't focus on the functionality, only getting the global function to be called within the anonymous function. I just used these for clarification and to simplify the issue. In actuality , I'm trying to use a helper function in Adobe DTM. The Anonymous function is actually a bigger function that runs as a data element.

OK, but most any javascript will not run after a -
   return

as the first element of the syntax unless there is a "container" to exit the code flow an "return"  to the code flow "out of" the container (method or function), so just have the function called as you first have it with out the "return" element, , as -

(function () {

Hi Slick, the code does get encapsulated by other JS code.

I had a syntax error on my side. This works as designed.