select2 demo

  $('.catalog').select2({
    placeholder: "--- Selected ---",
    ajax: {
    //for laravel csrf
      headers: {
          'X-CSRF-TOKEN': $('meta[name="csrf-token"]').attr('content')
      },
        url: 'api_url',
    type:'post',
    dataType: 'json',
    processResults: function (data) {
        return {
            results: data
        };
    },
    cache: true
  },
});

<select class="form-select catalog" name="catlog">
  <option value="{{$data->id}}" selected="selected">{{$data.name}}</option>
</select>

<?php
        isset($_REQUEST['q']) ? $name = $_REQUEST['q'] : $name = '';
        $row = ORM_DB::where('name', 'like', '%' . $name . '%')->get();
        foreach ($row as $key => $value) {
            $row_set[$key]["id"] = $value["id"];
            $row_set[$key]["text"] = $value["name"];
        }
        echo json_encode($row_set);
    }