get_blog_option()
return blog info by supplying blog id and blog option name.
So you may try changing the blog name variable from
$details->blogname to get_blog_option( $site->blog_id, 'blogdescription')
in the loop
Becauae get_blog_details() does not add the description from option to its output object. So it let is needed to manually fetch additional information.
By default, the get_blog_details() only returns the following details of the site
- blogname
- siteurl
- post_count
- home