Just figured good way to do it.
I tried passing the calling object's handle: ... uimenu(hcmenu, 'label' , 'Name', 'callback', UI_callbackHandler(hObject, handles)'); ...
But that is not available during execution. But I can pass a string, I chose the UI Tag
UITag = get(hObject, 'tag');
hcmenu = uicontextmenu;
uimenu(hcmenu, 'label' , 'Name', 'callback', ['UI_callbackHandler(''' UITag ''', handles)']);
set(hObject, 'uicontextmenu', hcmenu)
Now in my callback the first arg is the tag of the UI that tripped the callback.