Is there a Google Sheets formula to put the name of the sheet into a cell?

Question

The following illustration should help:

Answer 1

Here is my proposal for a script which returns the name of the sheet from its position in the sheet list in parameter. If no parameter is provided, the current sheet name is returned.

function sheetName(idx) {
  if (!idx)
    return SpreadsheetApp.getActiveSpreadsheet().getActiveSheet().getName();
  else {
    var sheets = SpreadsheetApp.getActiveSpreadsheet().getSheets();
    var idx = parseInt(idx);
    if (isNaN(idx) || idx < 1 || sheets.length < idx)
      throw "Invalid parameter (it should be a number from 0 to "+sheets.length+")";
    return sheets[idx-1].getName();
  }
}

You can then use it in a cell like any function

=sheetName() // display current sheet name
=sheetName(1) // display first sheet name
=sheetName(5) // display 5th sheet name

As described by other answers, you need to add this code in a script with :

Tools > Script editor