For JavaScript, I found the following workaround. Maybe it will help others.

I create a try-catch block. Within the try I provoke an exception, this one I catch-up with the catch and read-out the function name in the stack.

Note: this also works across several units -> USEUNIT

function getCaller(){
  let arrStackLines = [];

  try{
    throw new Error("throw a error to get the stack");
  }catch(objE){
    arrStackLines = objE.stack.split("\n");
  }
  let strLine = arrStackLines[arrStackLines.length -1];
  let intStart = strLine.indexOf("at ") + 3;
  let intEnd = strLine.indexOf("(<");
  Log.Message(strLine.substring(intStart, intEnd));
}

Best regards 

  meinTest GmbH

  www.meinTest.software

 SmartBear preferred value-added Service

 Provider in the DACH region

Targetted for 14.20, September 2019. 

We got it!

TestComplete 14.20 provides the CurrentTestCase property that returns information on the test case that is currently running. More information:

https://support.smartbear.com/testcomplete/docs/reference/program-objects/aqtestcase/currenttestcase.html