I have a main page (index.php) and if the client is not logged in, it redirect to the login.php.
header("Location: login.php");
The problem is that the search engines display as name the "example.com" instead of the title of the index or the login.
I am thinking if it is possible to do something like that.
header("Title: Example");
header("Location: login.php");
It sounds to me as though you want the Search Engine to index (and pick up the title) of your login page only - not the redirecting one, so set an HTTP status code in your redirect to inform them of the correct status of those pages.
I'd suggest using 302 (Found) - this will indicate to the Search Engines that - while the page exists - it's redirecting them (and non-logged in users) to another page - which is the one of interest.
Something like this:
header("Location: https://www.example.com/login.php", true, 302);
Then on your login page just set up the HTML correctly as you would otherwise including:
<head><title>Your Page Title</title></head>
Now search engines will not index the redirected page, but only the login page with your correctly set title.
You must set the title of a HTML document by using the <title> element inside the <head> element. You cannot do it via a HTTP response header.
<html>
<head>
<title>Example title</title>
</head>
<body>Some content</body>
</html>
Documentation: https://developer.mozilla.org/en-US/docs/Web/HTML/Element/title