Extract Array data in Javascript

When giving a return within a for, it implicitly applies a break so its repetition structure described above will stop at the first interaction.

It is very common to use this if you are looking for a specific value, or it will give a binary return.

So, since it is possible to have multiple groups, the solution is to accumulate in another array and return only the group names.

var grupos = [];
for (var x in $data.teste02){
   grupos.push($data.teste02[x].group_id.name);
}
return grupos ;

With this you could validate if the user is in a group using the indexOf for example.

if(grupos.indexOf('administrador') != -1){
  //Grupo administrador
}

If you want to create a new array with the names you can use .map() like this:

var grupos = $data.teste02.map(el => el.group_id.name);

So you get a new array, with the same size but only with group_id.name .

  

This is a new technology, part of the ECMAScript 2015 (ES6) standard.

As a curiosity, using generators is also possible to do basically following its logic. Here's an example:

function* get_group_names(data)
{
    for (let group of data.teste2) {
        yield group.group_id.name;
    }
}

Or alternatively, as commented by Sergio, use {group_id} in for , this being equivalent to group.group_by of previous code:

function* get_group_names(data)
{
    for (let {group_id} of data.teste2) {
        yield group_id.name;
    }
}

So, to get the list of group names, just convert the generator to array :

const groups = Array.from(get_group_names($data));

Or even traverse it through a loop of repetition:

for (let group of get_group_names($data)) {
    console.log(group);
}

References:

function * - JavaScript | MDN

for ... of - JavaScript | MDN

How does yield * work in Javascript?

See working below.

const $data = {
  'teste2': [{
    'group_id': {
      'name': 'Grupo 1'
    },

  }, {
    'group_id': {
      'name': 'Grupo 2'
    },

  }, {
    'group_id': {
      'name': 'Grupo 3'
    },

  }]
};

function* get_group_names(data) {
  for (let group of data.teste2) {
    yield group.group_id.name;
  }
}

// Converte o gerador para array:
console.log(Array.from(get_group_names($data)));

// Ou percorre o gerador com um laço de repetição:
for (let group of get_group_names($data)) {
  console.log(group);
}