I have a JSON like:
  var xx = {'name':'alx','age':12};
Now I can read the value of name which is 'alx' as xx[0].name, but how should I retrieve value of 'name' itself? By that, I mean how can I fetch the key at run time?
for (i in xx) {
    if (xx[i] == "alx") {
        // i is the key
    }
}
modified Code (from Victor) taking into account that you might want to look for any other possible string
var search_object = "string_to_look_for";
for (i in xx) {
    if (xx[i] == search_object) {
        // i is the key 
        alert(i+" is the key!!!"); // alert, to make clear which one
    }
}
You are looking for associative arrays in Javascript. A quick google search suggests the following:
Read this page http://www.quirksmode.org/js/associative.html
and especially this section http://www.quirksmode.org/js/associative.html#link5
xx[0].name, it'sxx.name. Or, more correct,xx["name"].xx["some key"]. This is valid, yet you can't access it likexx.some key. That's why I prefer to always use thexx["name"]notation.