How to remove duplicated items in array on Twig

Twig is a VIEW engine, and should not be used - in theory - to manipulate data. It's a (very) good practice to use (assumingly) PHP to gather data, do all necessary manipulations and then pass the right data to your view.

That said, here's how you can do it in pure Twig syntax:

{% set newArray = [] %}

{% for name in array %}
   {% if name not in newArray %}
     My name is {{name}}
   {% set newArray = newArray|merge([name]) %}
   {% endif %}


{% endfor %}

You can do it in one line since Twig 1.41 and 2.10:

{% set unique = array|reduce(
    (unique, item) => item in unique ? unique : unique|merge([item]), []
) %}

In your example:

{% for name in array|reduce((unique, item) => item in unique ? unique : unique|merge([item]), []) %}
     My name is {{name}}
{% endfor %}

In this case, as @Webberig said it's better to prepare your data before the rendering of the view. But when you have a more complex process and if is related to the view you can create a Twig Extension, with an extension the code would look like:

MyTwigExtension.php for Twig versions 1.12 and greater:

/**
 * {@inheritdoc}
 */
public function getFunctions()
{
    return array(
        new \Twig_SimpleFunction('array_unset', array($this, 'arrayUnset'))
    );
}

If you are on a Twig version earlier than 1.12, use this MyTwigExtension.php instead:

/**
 * {@inheritdoc}
 */
public function getFunctions()
{
    return array(
        'array_unset' => new \Twig_Function_Method($this, 'arrayUnset')
    );
}

/**
 * Delete a key of an array
 *
 * @param array  $array Source array
 * @param string $key   The key to remove
 *
 * @return array
 */
public function arrayUnset($array, $key)
{
    unset($array[$key]);

    return $array;
}

Twig:

{% set query = array_unset(query, 'array_key') %}