When you notice "Error establishing database connection" message while accessing your site, which means there is an issue with the connection string you have entered in your wp-config.php file.
Please open the wp.config.php file from the site root folder and make sure you have specified the correct database details, you have to check the following details:
Database hostname
Database name
Database username
Database password
You will get the above details from your database hosting provider where your database is hosted.