How can I use a php parameter in HTML markup?

So I have tried researching this before jumping into asking this question. Given that I have an index.php, and a cookie which stores the username, saved as $name, most answers tell me its simple to do this:

echo '<h3>'.$name.'</h3>'

But this doesnt work for me, and I assume its because im doing strange syntax for an if statement first, and I want to use the parameter within this if statement. My exact code looks more like this:

<?php 
  //store the cookie
  $name=$_COOKIE['user'];
  //check that it is set
  if(isset($_COOKIE['user'])): 
    <section id="login">
      <h1> Welcome</h1>
      echo '<h3>'.$name.'</h3>';
    </section>
  else: //prompt to login
  endif;
?>

It is meant to show a welcome message to a user that is logged in, adressing them by name, otherwise prompt the user to login.

So my question is: Why doesn't the parameter reflect at all? (shows nothing when the page is loaded) and How can I get this to work as intended?

ps. Please don't worry about the security risk of using cookies to do this etc. It is purposefully vulnerable.

pps. I am 100% sure the cookie is set, I viewed it with a cookie browser.