No, it apears as "Toplevel".

I'm not sure if the program.desktop file has something to do with that, but I didn't manage to get the application name from a desktop file to get used for Tkinter program. And I don't have any Tkinter or Tk app which would do what I'm trying to do.

For example, Firefox shows up as "Mozilla Firefox", but I don't see any X property with that value for Firefox window.. it might be something Mutter is doing.

Here is xprop for IDLE and Firefox:
$ sleep 5; xprop 
XKLAVIER_STATE(INTEGER) = 0, 0
WM_STATE(WM_STATE):
		window state: Normal
		icon window: 0x0
_NET_FRAME_EXTENTS(CARDINAL) = 1, 1, 23, 2
_NET_WM_DESKTOP(CARDINAL) = 0
_NET_WM_ALLOWED_ACTIONS(ATOM) = _NET_WM_ACTION_MOVE, _NET_WM_ACTION_RESIZE, _NET_WM_ACTION_FULLSCREEN, _NET_WM_ACTION_MINIMIZE, _NET_WM_ACTION_SHADE, _NET_WM_ACTION_MAXIMIZE_HORZ, _NET_WM_ACTION_MAXIMIZE_VERT, _NET_WM_ACTION_CHANGE_DESKTOP, _NET_WM_ACTION_CLOSE, _NET_WM_ACTION_ABOVE, _NET_WM_ACTION_BELOW
_NET_WM_STATE(ATOM) = 
WM_NORMAL_HINTS(WM_SIZE_HINTS):
		program specified minimum size: 1 by 1
WM_PROTOCOLS(ATOM): protocols  WM_DELETE_WINDOW
WM_HINTS(WM_HINTS):
		Client accepts input or input focus: True
		Initial state is Normal State.
_NET_WM_ICON_NAME(UTF8_STRING) = "Python Shell"
WM_ICON_NAME(STRING) = "Python Shell"
_NET_WM_NAME(UTF8_STRING) = "Python Shell"
WM_NAME(STRING) = "Python Shell"
WM_CLASS(STRING) = "42772672", "Toplevel"

$ sleep 5; xprop 
XKLAVIER_STATE(INTEGER) = 0, 0
WM_STATE(WM_STATE):
		window state: Normal
		icon window: 0x0
_NET_FRAME_EXTENTS(CARDINAL) = 0, 0, 24, 0
_NET_WM_DESKTOP(CARDINAL) = 0
_NET_WM_ALLOWED_ACTIONS(ATOM) = _NET_WM_ACTION_MOVE, _NET_WM_ACTION_RESIZE, _NET_WM_ACTION_FULLSCREEN, _NET_WM_ACTION_MINIMIZE, _NET_WM_ACTION_SHADE, _NET_WM_ACTION_MAXIMIZE_HORZ, _NET_WM_ACTION_MAXIMIZE_VERT, _NET_WM_ACTION_CHANGE_DESKTOP, _NET_WM_ACTION_CLOSE, _NET_WM_ACTION_ABOVE, _NET_WM_ACTION_BELOW
_NET_WM_STATE(ATOM) = _NET_WM_STATE_MAXIMIZED_HORZ, _NET_WM_STATE_MAXIMIZED_VERT
WM_HINTS(WM_HINTS):
		Client accepts input or input focus: True
		Initial state is Normal State.
		bitmap id # to use for icon: 0x1600094
		bitmap id # of mask for icon: 0x1600095
		window id # of group leader: 0x1600001
_NET_STARTUP_ID(UTF8_STRING) = "gnome-shell-17731-RD-OC-firefox-10_TIME71936264"
WM_WINDOW_ROLE(STRING) = "browser"
XdndAware(ATOM) = BITMAP
_MOTIF_DRAG_RECEIVER_INFO(_MOTIF_DRAG_RECEIVER_INFO) = 0x6c, 0x0, 0x5, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x10, 0x0, 0x0, 0x0
_NET_WM_ICON(CARDINAL) = 	Icon (16 x 16):
	 ░   ░▒▒▒▒░     
	 ▒▒░▒▒▒  ░▒▒▒   
	░▒░▒▒░▒  ░░▒░▒  
	░░░░░░▒▒▓░░▒░░▒ 
	▒░░░░░▒▒▓░░▒░ ░░
	▒░░░░░░▒░░░▒▒ ░░
	▒░░░░░░▒░▒▒▒▒ ░▒
	▒░░▒▒▒▒▓▒▒▒▒▒ ░▒
	▒░░░▒▒▓▒▒▒▒▒▒ ░▒
	░▒░░▒▒▒▒▒▒▓▓░░░░
	 ▒▒░░▒▒▒▒▓▒░░░▒░
	 ▒▒░░░░▒▒▒▒░░▒▒ 
	  ▒▒░░░░░░░░░▒  
	   ▒▒▒▒▒▒▒▒▒▒░  
	    ▒▒▒▒▒▒▒▒░   
	     ░░▒▒░░     

	Icon (32 x 32):
	            ░▒▒▒▓▒▒▒░           
	          ▒▒▒░     ░▒▒▒         
	        ░▓▒░         ░▒▒░       
	    ░  ▒▓▒░           ▒▒▒▒░     
	   ▒▒░▒▓▒▒░░░░        ░▒▒░▒░    
	   ▓▒▒▓▒▒▒▒▒▓░       ░░░▒▒ ▒▒   
	   ▓▒░░░░░▒▒▒░     ░░░░▒░░░ ▒▒  
	  ░▒░░░░░▒▒▓▒       ░░░░▓░  ░▒░ 
	  ▒▒░▒▒▒▒▒▒▒▒░░░     ░░░▒▒  ░░▒ 
	 ░▒░▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░▒▒▓░   ▒ 
	 ▒▒░▒▒▒▒▒▒▒▒░ ░▒░░░░░░░▒▒▓▒   ▒░
	 ▒▒▒▒▒▒▒▒▒▒░░▒▒▒░░░░▒▒▒▒▒▒▒░  ▒▒
	 ▓░▒▒▒▒▒▒▒░░░▒░░░░▒▒▒▒▒▒▓░▒░  ▒▓
	 ▓░▒▒▒▒▒▒▒▒░░▒▒▒▒▒▒▒▒▒▒▒▓▒    ▒▓
	 ▓░▒▒▒▒▒▒▓▓▓▓▒▒▒▒▒▒▒▒▓▓▓▓▒    ▒▓
	░▓▒▒▒▒▒▒▓▒▒▒▒▒▒▒▒▒▒▒▒▓▓▓▓▒ ░ ░▒▓
	 ▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▓▓▓▓▓▒ ░ ░░▒
	 ▒▒▒▒▒▒▒▒▒▒░░▒▒▒░░ ░▓▓▓▓▒░ ░░░░▒
	 ░▒▒▒▒▒▒▒▒▒▒░░░░░▒▒▒▓▓▓▓░░░░░░▒░
	  ▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▓▓▓▓▓▓▓░░░░░░▒ 
	  ▒▓▒▒▒▒▒▒░░▒▓▓▓▓▓▓▓▓▓▓▒░░░░░▒▒ 
	  ░▓▓▓▒▒▒▒░░░▒▓▓▓▓▓▓▓▓▒░░░░░▒▓░ 
	   ▒▓▓▓▒▒▒▒░░░░▒▓▓▓▓▒░░░░░▒▒▓▒  
	    ▓▓▓▒▒▒▒▒▒░░░░░░░░░░░░░░░▒░  
	    ░▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░▒░   
	     ▒▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒░░░░▒▒    
	      ▒▓▓▓▓▒▒▒▒▒▒▒░░░░░▒▒▒▒     
	      ░▒▓▓▓▓▒▒▒▒▒▒▒▒░░░▒▒▒░     
	       ░▒▒▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒░░     
	        ░░▒▒▒▓▓▓▓▓▓▒▒▒▒░░       
	          ░░▒▒▒▒▒▒▒▒▒░░         
	                                

	Icon (48 x 48):
	                  ░▒▒▓▓▓▓▓▒▒░                   
	               ░▒▓▓▒░░    ░░▒▓▒░                
	             ▒▓▓▒             ▒▓▓▒              
	           ░▓▓▒░               ░░▒▓░            
	          ▒▓▓▒░                ░░ ░▓▒           
	    ░░  ░▓▓▓▒▒░░                ░▒  ▒▓░         
	    ▒░ ░▓▓▓▒▒░░░░░░             ░░▒░ ░▒▒        
	   ░░░░▓▓▓▓▒▒▒░▒▒▒░            ░░░▒▒░  ▒▒       
	   ▒░▒▒▒▓▒▒▒▒▒▒▒▒░             ░░▒░░▒   ▒▒      
	   ▒▒▒▒░░░░░░▒▒▒▒░          ░░░░░▒▒░ ░   ▒░     
	   ▒▒▒░░▒▒▒░▒▒▒▒▒░          ░░░░░░▒▒     ░▒     
	   ▒░░░▒▒▒▒▒▒▒▒▒▒░           ░░░░░░▒▒     ▒░    
	   ▒░▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░         ░░░░▒▓░  ░ ░     
	   ░▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒      ░░░░░░▒▒▒   ░      
	  ░░▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░▒░░░░░░░░░░▒▒▒▒▓          
	  ░▒▒▒▒▒▒▒▒▒▒▒▒▒▒░   ░▒░░░░░░░░░░▒▒▒▒▓░         
	 ░░▒▒▒▒▒▒▒▒▒▒▒▒░░   ▒▒▒░░░░░▒▒▒░░▒▒▒▒▓░     ░   
	 ░░▒▒▒▒▒▒▒▒▒▒▒▒░░░░▒▒░░░░░░░▒▒▒▒▒▒▒▓▒▒▒░░   ░░  
	 ░░▒▒▒▒▒▒▒▒▒▒▒░░░░▒▒░░░░░░▒▒▒▒▒▒▒▒▒▓▒ ▒ ░░  ░▒░ 
	 ░▒▒▒▒▒▒▒▒▒▒░░░░░░▒░░░░░░▒▒▒▒▒▒▒▒▒▒▓▒   ░░  ░▒▒ 
	 ░▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▓▓▓    ░  ░▓▒ 
	 ░▒▒▒▒▒▒▒▒▒▓▓▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▓▓▓▓▓       ░▓▒ 
	 ▒▒▒▒▒▒▒▒▒▒▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▓▓▓▓▓▓▓   ░   ▒▒░ 
	░▒▒▒▒▒▒▒▒▒▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▓▓▓▓▓▓▓░  ░  ░▒░░ 
	░▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▓▓▓▓▓▓▓▓░ ░░ ░░░░░ 
	░▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░▒▒▒▒▒▒░░░░▒▒▓▓▓▓▓▓▒▒░  ░░░░░░  
	 ▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░▒▒░░░░░  ▒▒▓▓▓▓▓▒░░  ░░░░░░  
	 ░▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░▒▒▒░▒▓▓▓▓▓▓░░░ ░░░░░░░  
	 ░▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░▒▒▒▒▒▓▓▓▓▓▓▓▓▓░░░░░░░░░▒   
	  ▒▒▓▒▒▒▒▒▒▒▒▒▒▒▓▓▒▒▒▒▒▒▓▓▓▓▓▓▓▓▓▓▒░░░░░░░░▒░   
	  ░▒▓▒▒▒▒▒▒▒▒▒▒░▒▒▓▒▓▓▓▓▓▓▓▓▓▓▓▓▓▓░░░░░░░░░▒░   
	   ▒▓▓▒▒▒▒▒▒▒░░░░▒▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▒░░░░░░░░▒▒░   
	   ▒▒▓▓▓▒▒▒▒▒▒░░░░░▒▒▓▓▓▓▓▓▓▓▓▓▒▒░░░░░░░░░▒▒    
	    ▒▓▓▓▒▒▒▒▒▒▒░░░░░░▒▓▓▓▓▓▓▓▒░░░░░░░░░░░▒▓░    
	    ▒▓▓▓▓▒▒▒▒▒▒▒▒░░░░░░▒▒▒▒▒░░░░░░░░░░░▒▒▒░     
	     ▒▓▓▓▓▒▒▒▒▒▒▒▒▒░░░░░░░░░░▒▒░░░░░░░▒▒░░      
	     ░▒▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░▒░░░░░░░░      
	      ░▒▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░       
	       ░▓▓▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░        
	        ░▒▓▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒░░░░░░░░░░░░░         
	         ░▒▒▓▓▓▓▒▒▒▒▒▒▒▒▒░░░░░░░░░▒▒▒▒          
	         ░░▒▒▒▓▓▓▓▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░         
	         ░░░▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░▒▒▒▒░░          
	          ░░░▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░▒▒▒░░           
	            ░░░▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒░░░            
	              ░░░░▒▒▒▒▒▒▒▒▒▒░░░░░               
	                  ░░░░░░░░░░░                   
	                                                


_NET_WM_SYNC_REQUEST_COUNTER(CARDINAL) = 23068819
_NET_WM_WINDOW_TYPE(ATOM) = _NET_WM_WINDOW_TYPE_NORMAL
_NET_WM_USER_TIME_WINDOW(WINDOW): window id # 0x1600092
WM_CLIENT_LEADER(WINDOW): window id # 0x1600001
_NET_WM_PID(CARDINAL) = 24976
WM_LOCALE_NAME(STRING) = "lv_LV.utf8"
WM_CLIENT_MACHINE(STRING) = "RD-OC"
WM_NORMAL_HINTS(WM_SIZE_HINTS):
		program specified minimum size: 0 by 0
		window gravity: NorthWest
WM_PROTOCOLS(ATOM): protocols  WM_DELETE_WINDOW, WM_TAKE_FOCUS, _NET_WM_PING, _NET_WM_SYNC_REQUEST
WM_CLASS(STRING) = "Navigator", "Firefox"
WM_ICON_NAME(STRING) = "Issue 13553: Tkinter doesn't set proper application name - Python tracker - Mozilla Firefox"
_NET_WM_ICON_NAME(UTF8_STRING) = "Issue 13553: Tkinter doesn't set proper application name - Python tracker - Mozilla Firefox"
WM_NAME(STRING) = "Issue 13553: Tkinter doesn't set proper application name - Python tracker - Mozilla Firefox"
_NET_WM_NAME(UTF8_STRING) = "Issue 13553: Tkinter doesn't set proper application name - Python tracker - Mozilla Firefox"