Update/Edit List title using Javascript Sharepoint.

var oList="";
var Listname="Document Sharing";
var NewTitle="Sharing Documents";
function updateList() {
    var clientContext = new SP.ClientContext.get_current();
    var oWebsite = clientContext.get_web();
    oList = clientContext.get_web().get_lists().getByTitle(Listname);
   this.oList.set_title(NewTitle);
oList.update();
    clientContext.load(oList);
    clientContext.executeQueryAsync(Function.createDelegate(this, this.onQuerySucceeded), Function.createDelegate(this, this.onQueryFailed));
}

function onQuerySucceeded() {
    var result ="List title updated to"+ oList.get_title() + '.';
    alert(result);
}

function onQueryFailed(sender, args) {
    alert('Request failed. ' + args.get_message() + '\n' + args.get_stackTrace());
}

updateList("Test");