Abhishek,
Normally you would handle the renaming in your mxd that is used for that map service. I you have to do it in your code then you will have to do that through direct DOM manipulation. You need to find the DOM element using the id or some class and then change the innerHTML text (lines 9 and 10 in the showLayers function of the LayerList widget.js).
showLayers: function() {
this.layerListView = new LayerListView({
operLayerInfos: this.operLayerInfos,
layerListWidget: this,
config: this.config
}).placeAt(this.layerListBody);
var node = query(".layer-title-div-LOJIC_PublicSafety_Louisville_7908_0")[0]
node.innerHTML = "Em Sirens";
},