[Hoshinokoe]

Dimaz,

Как-то так:

if (!Array.prototype.filter)
{
  Array.prototype.filter = function(fun)
  {
    var len = this.length;
    if (typeof fun != "function")
      throw new TypeError();

    var res = new Array();
    var thisp = arguments[1];
    for (var i = 0; i < len; i++)
    {
      if (i in this)
      {
        var val = this[i]; 
        if (fun.call(thisp, val, i, this))
          res.push(val);
      }
    }

    return res;
  };
}

var data = [{"name":"Dmitry", "lastname":"Ivanov"},{"name":"Dmitry", "lastname":"Petrov"}, {"name":"Dimaz", "lastname":"Petrov"}];
var filtered  = data.filter(function (element, index, array)
{
    return element.name == "Dmitry";
});

P.S. если юзать jquery, то так:

var arr = jQuery.grep(data , function (element, index) { return element.name == "Dmitry"; });