Edit in JSFiddle

var list = {
    'friends': {
        'fred': '123-4567',
        'lisa': '123-6789'
    },
    'work': {
        'joe': '234-5678'
    }
};

/* original function */
function old_addName(group, name, number) {
    if (list[group] && list[group][name]) {
        list[group][name] = number;
    } else {
        if (list[group]) {
            list[group][name] = number;
        } else {
            list[group] = {};
            list[group][name] = number;
        }
    }
}

/* more efficient function */
function addName(group, name, number) {
    if (!list[group]) {
        list[group] = {};
    }
    list[group][name] = number;
}

/****************
 * Demo stuff
 ****************/
function showContacts(){
    var t = '';
    $.each(list, function(g){
        t += '\n' + g.toUpperCase() + '\n=======\n';
        $.each(list[g], function(n){
            t += n + ' : ' + list[g][n] + '\n';
        });
    });
    $('textarea').val(t);
}
$('button').click(function(){
    var i = $('input'),
        t = ($(this).attr('data-test') || ',,').split(','),
        g = i.eq(0).val() || t[0],
        n = i.eq(1).val() || t[1],
        b = i.eq(2).val() || t[2];
    if (g && n && b) {
        addName(g.toLowerCase(), n, b);
        showContacts();
    }
    i.val('');
});
showContacts();

Group: <input type="text" placeholder="Enter a group"><br>
Name : <input type="text" placeholder="Enter a name"><br>
Number: <input type="text" placeholder="Enter the number"><br>
<button>Add</button> <button data-test="emergency,Police,911">Add Police</button><br>
<br>Contacts<br>
<textarea readonly rows="20" cols="30"></textarea>