Display an icon with get_post_meta?

The syntax for get_post_meta that you are using in incorrect. It is documented here.

You need to pass a string for the second parameter. So, for example, use

$icon = get_post_meta( $post->ID, 'apaitei_logariasmo_facebook', true );

Instead of

$icon = get_post_meta( $post->ID, apaitei_logariasmo_facebook, true );

In addition, string literals must be between the quotes in PHP.

if( $icon == esc_attr( 'Ναι' ) ) :

So, the solution is:

<?php
$icon = get_post_meta( $post->ID, 'apaitei_logariasmo_facebook', true );
if( $icon == esc_attr( 'Ναι' ) ) : ?>
<span class="facebook-badge"></span>
<?php endif; ?>