Take a look at How do I change the welcome message in Magento 1.9+ the proper way?

Then make changes to

/**
 * Get block messsage
 *
 * @return string
 */
protected function _toHtml()
{
    if (empty($this->_data['welcome'])) {
        if (Mage::isInstalled() && Mage::getSingleton('customer/session')->isLoggedIn()) {
            //change from
            //$this->_data['welcome'] = $this->__('Welcome, %s!', $this->escapeHtml(Mage::getSingleton('customer/session')->getCustomer()->getFirstname()));
            //to
            $this->_data['welcome'] = $this->__('hi visitor, welcome to %s! . <a href="%s">Log in</a> or <a href="%s">register</a>', $this->escapeHtml(Mage::app()->getStore()->getName();), Mage::helper('customer')->getLoginUrl(),Mage::helper('customer')->getRegisterUrl();
        }

Take a look at How do I change the welcome message in Magento 1.9+ the proper way?

Then make changes to

/**
 * Get block messsage
 *
 * @return string
 */
protected function _toHtml()
{
    if (empty($this->_data['welcome'])) {
        if (Mage::isInstalled() && Mage::getSingleton('customer/session')->isLoggedIn()) {
            //change from
            //$this->_data['welcome'] = $this->__('Welcome, %s!', $this->escapeHtml(Mage::getSingleton('customer/session')->getCustomer()->getFirstname()));
            //to
            $this->_data['welcome'] = $this->__('hi visitor, welcome to %s! . <a href="%s">Log in</a> or <a href="%s">register</a>', $this->escapeHtml(Mage::app()->getStore()->getName();), Mage::helper('customer')->getLoginUrl(),Mage::helper('customer')->getRegisterUrl();
        }