Hi, no, I have not given them my notice yet but I am expecting them to ask who I am moving to. As it is a competitor, I would rather not tell them (they will find out anyway after I leave I'm sure). It would just avoid any awkward conversations before I leave.
What I really want to know is whether they can then make my life difficult if there is no clause in my contract saying that I cannot work for a competitor. (aside from the obvious of not breaching their intellectual property rights).