Change Name Category programmaticaly

changeCategoryName.php

<?php
/** Location : Namespace/module/data/namespace_module_setup/install-0.1.0.php
try {
    
    $storeId = 4 // your target store;
    /**
     * Set the right Store
     */
    Mage::app()->setCurrentStore($storeId);
    $_helperCategory = Mage::helper('catalog/category');
    /**
     * Retrieves the categorie of the current store
     */
    $cats = $_helperCategory->getStoreCategories();
    /**
     * Switch to the Admin Store to save
     */
    Mage::app()->setCurrentStore(Mage_Core_Model_App::ADMIN_STORE_ID);
    $categoryModel = Mage::getModel('catalog/category');
    foreach ($cats as $cat) {
    /** retrieves your category by what you want */
        if ($cat->getName() == 'Old Custom Name') {
            $categoryModel->setStoreId(0);
            $categoryModel->load($cat->getId());
            $categoryModel->setName('My New Custom Name')->save();
        }
    }

} catch (Exception $e) {
    // Silence is golden
    Mage::logException($e);
}