if(isset($_POST['btn-save'])){
    $resource = Mage::getSingleton('core/resource');
    $readConnection = $resource->getConnection('core_read');
    $table = $resource->getTableName('catalog/product');
    $search = $_POST['gsearch'];
    $query = 'SELECT * FROM ' . $table . 'WHERE name LIKE' .$search.'';
    $results = $readConnection->fetchAll($query);
     foreach($results as $res){
        echo $res ['name'];
     }
}

if ($this->getRequest()->isPost() && $this->getRequest()->getPost('btn-save')) {

    $collection = Mage::getResourceModel('catalog/product_collection');
    $collection->addAttributeToSelect('name');
    $collection->addAttributeToFilter('name',array('like'=> '% '.$this->getRequest()->getPost('gsearch').' %'));
    $names = $collection->getColumnValues('name');


}