public function getCustomer()
{
  return $this->hasOne(Customer::className(), ['id' => 'customer_id']);
}

class OrderSearch extends Order
{
  public $customer_name; //<=====就是加在这里
}

public function search($params)
{
  $query = Order::find();
  $query->joinWith(['customer']);<=====加入这句
  $dataProvider = new ActiveDataProvider([
    'query' => $query,
  ]);
  
  $dataProvider->setSort([
    'attributes' => [
      /* 其它字段不要动 */  
      /* 下面这段是加入的 */
      /*=============*/
      'customer_name' => [
        'asc' => ['customer.customer_name' => SORT_ASC],
        'desc' => ['customer.customer_name' => SORT_DESC],
        'label' => 'Customer Name'
      ],
      /*=============*/
    ]
  ]); 

  if (!($this->load($params) && $this->validate())) {
    return $dataProvider;
  }

  $query->andFilterWhere([
    'id' => $this->id,
    'user_id' => $this->user_id,
    'customer_id' => $this->customer_id,
    'order_time' => $this->order_time,
    'pay_time' => $this->pay_time,
  ]);

  $query->andFilterWhere(['like', 'status', $this->status]);
   $query->andFilterWhere(['like', 'customer.customer_name', $this->customer_name]) ;//<=====加入这句
  
  return $dataProvider;
}

<?= GridView::widget([
  'dataProvider' => $dataProvider,
  'filterModel' => $searchModel,
  'columns' => [
    ['class' => 'yii\grid\SerialColumn'],
    'id',
    'customer_id', 
    'status',
    ['label'=>'客户', 'attribute' => 'customer_name', 'value' => 'customer.customer_name' ],//<=====加入这句
    ['class' => 'yii\grid\ActionColumn'],
  ],
]); ?>