Create shortcode to display specific post in relationship current date

Try this use your desired name for function names :

function main_func_name() {

    //Date parameter
    $currentDay = date('j');
    $currentMonth = date('n');
    //wp query to show saints name 
    $con = mysqli_connect("localhost", "mydb", "mypassword", "myuser");
    if (mysqli_connect_errno()) {
        echo "Failed to connect to MySQL: " . mysqli_connect_error();
    }
    $sql = "select * from santi where numero_giorno= " . $currentDay . " and numero_mese= " . $currentMonth;
    $result = mysqli_query($con, $sql);
    if (mysqli_affected_rows($con) > 0) {
        while ($row = $result->fetch_assoc()) {
            ?>
                         <span id="txtSaintName"><?php echo $row['nome'] ?></span>
            <?php
        }
        mysqli_close($con);
    }
}

add_shortcode('shortcode_name', 'function_shortcode');

function function_shortcode() {
    ob_start();
    main_func_name();
    return ob_get_clean();
}
?>