This line is your problem:
$new_site_name = $site_name . '<sup>echo '<img src="' . plugins_url( 'images/wordpress.png' ,"logo.jpg" ) . '" > '</sup>';
Here you’ve muddled up the quotes and put PHP code inside a string expecting it to still work.
e.g.
echo ' this is inside a quote:' inside a quote ' . ';
It doesn’t work because the quote in your string closes the starting quote, ending the string. To fix this you need to either:
- use a double quote
- escape your characters
e.g.
echo 'this is inside a quote \' inside a quote \' .';
As a side note, make sure that your code editor supports syntax highlighting with a good colour scheme, it will make these kinds of issues more obvious.