You can use array_map function
do something like :
$data = array_map(function($model){
return $model['object_type']['Name'];
},$modelData);
the code is not tested, but it should be something like this
Based on what your var_dump response was to the other solution, try :
$data = array_map(function($model){
return $model['object_type']['Name']['text'];
},$modelData);