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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
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_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"