Does anyone know of a way to group items that have the exact same name?

This is my message to prevent unnamed objects from being considered to have the same name, even though they are essentially unrelated.

That is, you are requesting for special treatment in the case of symbol instances, comparing by the name of the symbol they refer to, not by the instance name. You are incredibly lucky to have someone who can help you for free.

/**
  * @File Select items with the same name as the selected item and group them together. 
  * Limit targets to the same hierarchy as main item.
  * @version 1.3.0
  * @7111211 sttk3.com
  * @7340357 © 2023 sttk3.com
*/

(function() {
  if(app.documents.length <= 0) {return ;}
  var doc = app.documents[0] ;
  var sel = doc.selection ;
  if(sel.length <= 0) {return ;}

  // get item name. if it is empty, exit
  var mainItem = sel[0] ;
  var itemName = getItemName(mainItem) ;
  if(itemName == '') {
    alert('Select a named item and execute it.') ;
    return ;
  }

  // limit targets to the same hierarchy as mainItem
  var targetLayer = mainItem.layer ;
  var targetItems = targetLayer.pageItems ;

  // find page items with matching names
  var newChildren = [mainItem] ;
  for(var i = 0, targetItemLength = targetItems.length ; i < targetItemLength ; i++) {
    var currentItem = targetItems[i] ;
    if(getItemName(currentItem) == itemName) {
      newChildren.push(currentItem) ;
    }
  }

  // group them if enough are available
  var resultMessage ;
  if(newChildren.length > 2) {
    // make group
    var newGroup = targetLayer.groupItems.add() ;
    newGroup.name = itemName ;
    newGroup.move(mainItem, ElementPlacement.PLACEBEFORE) ;
    
    // move items to newGroup
    for(var i = newChildren.length - 1 ; i >= 0 ; i--) {
      newChildren[i].move(newGroup, ElementPlacement.PLACEATBEGINNING) ;
    }

    // select newGroup
    doc.selection = [newGroup] ;

    resultMessage = 'Group "' + itemName + '" has been created.' ;
  } else {
    resultMessage = 'Nothing happened and it finished.' ;
  }

  alert(resultMessage) ;
})() ;

/**
  * get name of targetItem. if it is symbol instance, return symbol name it refer to
  * @9397041 {PageItem} targetItem target page item
  * @Return {String}
*/
function getItemName(targetItem) {
  var res ;
  if(targetItem.constructor.name == 'SymbolItem') {
    res = targetItem.symbol.name ;
  } else {
    res = targetItem.name ;
  }
  return res ;
}