Multiple if conditions

The contents of text layer is not the same as its name. The contents layer is that, what you asked in:

Script, copying text layers contents to clipboard

btw the script in other thread does what you want here (when changing the goal to names from contents).

Regarding currect script from original post, change '=' characters to '==', or use:

aLs = [].slice.call(activeDocument.activeLayer.artLayers), nms = ''
while(aLs.length) nms += aLs.shift().name + ' '; nms.slice(0, -1)

Using case seems to work!

#target photoshop;

var thedoc = app.activeDocument;
app.activeDocument.activeLayer = app.activeDocument.layerSets.getByName("Text");

 var myLayerName = activeDocument.activeLayer.name; 
 
 var textlayersnum = activeDocument.activeLayer.artLayers.length ;
//alert(textlayersnum);
 
switch ( textlayersnum) {
  case 1:
 var name1 = activeDocument.activeLayer.artLayers[0].name;
 
    break;
  case 2:
  var name1 = activeDocument.activeLayer.artLayers[0].name;
var name2 = activeDocument.activeLayer.artLayers[1].name;
var newname = (name1 +" " +name2);
    break;
  case 3:
var name1 = activeDocument.activeLayer.artLayers[0].name;
var name2 = activeDocument.activeLayer.artLayers[1].name;
var name3 = activeDocument.activeLayer.artLayers[2].name;
var newname = (name1 +" " +name2 +" " +name3);
   
    break;
  case 4:
  
   var name1 = activeDocument.activeLayer.artLayers[0].name;
var name2 = activeDocument.activeLayer.artLayers[1].name;
var name3 = activeDocument.activeLayer.artLayers[2].name;
var name4 = activeDocument.activeLayer.artLayers[3].name;
var newname = (name1 +" " +name2 +" " +name3 +" " +name4); 
 
    break;
  case 5:
   var name1 = activeDocument.activeLayer.artLayers[0].name;
var name2 = activeDocument.activeLayer.artLayers[1].name;
var name3 = activeDocument.activeLayer.artLayers[2].name;
var name4 = activeDocument.activeLayer.artLayers[3].name;
var name5 = activeDocument.activeLayer.artLayers[4].name;
var newname = (name1 +" "+name2 +" "+name3 +" " +name4 +" " +name5); 

    break;
  case 6:
var name1 = activeDocument.activeLayer.artLayers[0].name;
var name2 = activeDocument.activeLayer.artLayers[1].name;
var name3 = activeDocument.activeLayer.artLayers[2].name;
var name4 = activeDocument.activeLayer.artLayers[3].name;
var name5 = activeDocument.activeLayer.artLayers[4].name;
var name6 = activeDocument.activeLayer.artLayers[5].name;
var newname = (name1 +" " +name2 +" " +name3 +" " +name4 +" " +name5 +" " +name6 );
  
    break;
  case 7:
var name1 = activeDocument.activeLayer.artLayers[0].name;
var name2 = activeDocument.activeLayer.artLayers[1].name;
var name3 = activeDocument.activeLayer.artLayers[2].name;
var name4 = activeDocument.activeLayer.artLayers[3].name;
var name5 = activeDocument.activeLayer.artLayers[4].name;
var name6 = activeDocument.activeLayer.artLayers[5].name;
var name7 = activeDocument.activeLayer.artLayers[6].name;
var newname = (name1 +" " +name2 +" " +name3 +" " +name4 +" " +name5 +" " +name6 +" " +name7);
  
} 
   alert(newname);