Hello Friends, I have seen many posts but i can't find the exact solution for this issue and then i have investigate code of the default magento. So Please follow the below steps for getting the exact result as you want.

1. Go to app/code/core/Mage/CatalogSearch/Model/Resource/fulltext.php

2. Then search the below code it is approximately at 382 line

if ($likeCond != '' && $searchType == Mage_CatalogSearch_Model_Fulltext::SEARCH_TYPE_LIKE) {
    $select->columns(array('relevance'  => new Zend_Db_Expr(0)));
    $where = $likeCond;
}

3. And change with the below code.

if ($likeCond != '' && $searchType == Mage_CatalogSearch_Model_Fulltext::SEARCH_TYPE_LIKE) {
     $select->columns(array('relevance'  => new Zend_Db_Expr(0)));
    //$where = $likeCond;
    $where .= ($where ? ' AND ' : '') . $likeCond;
}

4. Clear all the cache. After following the above steps, please search any product name and you will get the exact product which you want. I hope this is really help you. Thanks,