Display the new message and clear the previous messages on every page using Message Manager.

Create the event.xml in your module and add the below code

<?xml version="1.0"?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:Event/etc/events.xsd">
    <event name="layout_render_before">
      <observer name="success_message" instance="VendorModuleObserverMessageObserver" shared="false" />
  </event>
</config>

Create the MessageObserver.php file in the Observer directory

<?php
namespace VendorModuleObserver;

use MagentoFrameworkEventObserverInterface;
use MagentoFrameworkEventObserver;

class MessageObserver implements ObserverInterface
{
    public function __construct(       
        MagentoFrameworkMessageManagerInterface $messageManager,
    )
    {    
        $this->messageManager = $messageManager;   
    }
    public function execute(Observer $observer)
    {
        $this->messageManager->getMessages(true); //this will clear your messageManager container
        $this->messageManager->addSuccess(__('Add Custom message here'));
        return $this;
    }
}