Pulling data in JSON

You have to iterate the keys of the data property. You can use Object.keys or for(var key in object) .

An example would be:

var data = {
  "type": "champion",
  "format": "standAloneComplex",
  "version": "7.18.1",
  "data": {
    "Aatrox": {
      "id": "Aatrox",
      "key": "266",
      "name": "Aatrox",
      "title": "a Espada Darkin",
      "image": {
        "full": "Aatrox.png",
        "sprite": "champion0.png",
        "group": "champion",
        "x": 0,
        "y": 0,
        "w": 48,
        "h": 48
      }
    },
    "Viktor": {
      "id": "Viktor",
      "key": "112",
      "name": "Viktor",
      "title": "o Arauto das Máquinas",
      "image": {
        "full": "Viktor.png",
        "sprite": "champion4.png",
        "group": "champion",
        "x": 0,
        "y": 0,
        "w": 48,
        "h": 48
      }
    }
  }
};
var arr = []; // não sei bem porque precisas disto? é só para o exemplo pois já tens outra "arr no código que vais acrescentar com "data"?
arr.push(data);
for (var i = 0; i < arr.length; i++) {
  var obj = arr[i].data;
  Object.keys(obj).forEach(function(prop) {
    if (obj[prop].key == 266) {
      console.log(obj[prop].name);
    }
  });
}

Notice that your JSON returns the value of key in String! So you can not use === if you compare with a number. Or use a string like this: if (obj[prop].key == '266') {

I was able to make callback work. But I made a function called champion () where it will just add id , find the name and thus return the value.

But this return obj[prop].name; is bringing results like undefined . Testing console.log(obj[prop].name) is working perfectly. But why does the value return as undefined ?

function callback(andress, fn){        
    $.ajax({
        url: andress,
        type: 'GET',
        dataType: 'json',
        error: function(){},
        success: fn
    });
}

function champion(id) {
    callback('http://ddragon.leagueoflegends.com/cdn/7.18.1/data/pt_BR/champion.json', function(retorno) {
        var arr = [];
        arr.push(retorno);
        for (var i = 0; i < arr.length; i++) {
            var obj = arr[i].data;
            Object.keys(obj).forEach(function(prop) {
                if (obj[prop].key == id) {
                    return obj[prop].name;
                }
            });
        }
    });
}

callback(url+'/lol/summoner/v3/summoners/by-name/'+hash.name+'?api_key='+key, function(retorno) {
    callback(url+'/lol/match/v3/matchlists/by-account/'+retorno.accountId+'/recent?api_key='+key, function(invocador) {
        var itens = '';
        for (var i = 0; i < invocador.matches.length; i++) {
            itens += '<li>'+champion(invocador.matches[i].champion)+'</li>';
        }
        $('.partidas_recentes').html(itens);
    });

    $('.mdl-layout-title').text(retorno.name);
});