Minor drawback with Crockford Prototypical Inheritance

Question

Just experimenting with different inheritance techniques in JS, and came across something mildly discomfiting about Crockford's Prototypal Inheritance pattern:

function object(o) {
    function F() {}
    F.prototype = o;
    return new F();
}

var C,
    P = {
         foo:'bar',
         baz: function(){ alert("bang"); }
         }

C = object(P);

It's all good - except when you log to console - the object appears as F. I've seen classical emulation in which you can repoint the constructor - is there a similar method to coerce the objects (console) reference?