Is it possible to set up to search name of attached document or better yet, contents of attach doc?
If you are on WordPress, there are at least of couple of plugins that do full-text search on files:


https://searchwp.com/
https://wordpress.org/plugins/opensearchserver-search/


Since the files uploaded with CiviCRM are stored in the same folder hierarchy as the other WordPress uploads those plugins should be able to index and locate these files.

However, they will not be able to link the document back to the CiviCRM contact they are attached to. This feature could be achieved with a custom development.