Any way to identify browser tab in JavaScript?

SessionStorage is per tab/window, so you can define a random number in sessionStorage and get it at first if exists:

var tabID = sessionStorage.tabID ? 
            sessionStorage.tabID : 
            sessionStorage.tabID = Math.random();

UPDATE:
In some cases, you may have same sessionStorage in multiple tabs (e.g. when you duplicate tab). In that case, following code may help:

var tabID = sessionStorage.tabID && 
            sessionStorage.closedLastTab !== '2' ? 
            sessionStorage.tabID : 
            sessionStorage.tabID = Math.random();
sessionStorage.closedLastTab = '2';
$(window).on('unload beforeunload', function() {
      sessionStorage.closedLastTab = '1';
});