Normally you shouldn't execute any functions inside an echo. It's better to do all "preparations" in advance and echo the results. That way it's simpler to split the logic and the presentation later
<?php
if( is_page( 3769 ) ):
echo 'ANOTHER LOGO';
else:
$categories = get_the_category();
$cat_slug = $categories[0]->slug;
echo <<<HTML
<a href="$home_url"><img border="0" src="http://WEBSITE.COM/logo{$cat_slug}.png" width="500" height="100"></a>
HTML;
endif;
?>