You’re missing the <?php tag before the closing bracket, so it’s not being processed. Your code updated below:
<?php if ( is_singular('customer') ) { ?>
<img src="https://wordpress.stackexchange.com/questions/312935/<?php bloginfo("template_directory'); ?>/dist/images/logo-customer.png" alt="Logo Customer">
<?php } else { ?>
<img src="https://wordpress.stackexchange.com/questions/312935/<?php bloginfo("template_directory'); ?>/dist/images/logo.png" alt="Logo">
<?php } ?>