Should I use unnamed or named functions?
So this is redundant.

var openIPP = function openIPP() {
    $IPPNonDefault.stop().animate({"height": OpenHeight}, DownRate);
}


Because both of these functions are the same.

var openIPP = function() {
    $IPPNonDefault.stop().animate({"height": OpenHeight}, DownRate);
}
function openIPP() {
    $IPPNonDefault.stop().animate({"height": OpenHeight}, DownRate);
}


This is the easiest for me to read.

$IPPWrapper.hover(
    function() {
        $IPPNonDefault.stop().animate({"height": OpenHeight}, DownRate);
    },
    function() {
        $IPPNonDefault.stop().animate({"height": "0px"}, UpRate);
    }
);


But if you want more information in case a bug is thrown then use named functions like so.

$IPPWrapper.hover(
    function openIPP() {
        $IPPNonDefault.stop().animate({"height": OpenHeight}, DownRate);
    },
    function closeIPP() {
        $IPPNonDefault.stop().animate({"height": "0px"}, UpRate);
    }
);