Google Sheets Script to return sheet name will not automatically update on creating a new sheet

Question

I have written a script in Google Sheets to return the name of a given sheet (see below).

The function is written into a summary sheet, where the input given as the index of the sheet required. I have all the functions pre-written e.g.

A1 = GetSheet(1) B1 = GetSheet(2) C1 = GetSheet(3) ...etc

Obviously, when the sheet with the index in question does not yet exist, I get an error. However, when I do create that sheet, the cell does not automatically update with the name of the new sheet, it still returns an error. To get the name to appear, I have to delete the function and re-paste it in.

Is there a way for the cells to automatically update when a new sheet is added, without re-typing the function?

Apologies if I am missing something obvious, I am very new to this!

function GetSheet(input)
{
  var spread = SpreadsheetApp.getActiveSpreadsheet();
  var sourceSheet = SpreadsheetApp.getActiveSheet();
  var sourceIndex = sourceSheet.getIndex();
  var nextIndex = sourceIndex + 1;  
  var ss = SpreadsheetApp.getActiveSpreadsheet();
  SpreadsheetApp.setActiveSheet(ss.getSheets()[input]);        
  var active = ss.getActiveSheet();
  var name = active.getName();                                   
  return name
}

Answer 1

Not Changing because their inputs are not changing

The reason that your custom functions are not returning anything when you create another sheet is because the input to these kinds of function are generally expected to be cell references and the functions will recalculate when the value of those cell references change. But your inputs are just numbers (indexes to the allSheets() array and creating another sheets doesn't change any of their inputs so they never get a chance to run. I don't think that creating a new sheet will trigger an onChange I think these are the only things that trigger an onChange event.

EDIT, INSERT_ROW, INSERT_COLUMN, REMOVE_ROW, REMOVE_COLUMN, INSERT_GRID, REMOVE_GRID, FORMAT and OTHER

Admittedly, I don't know what OTHER is so maybe there's hope.