How can I find specific block name in structure->blocks in drupal-7?
You could enable the contextual links module and hover over the block and click the small gear icon to edit the block.
you could figure out what region the block is in using firebug or similar which will narrow it down in the block administration page assuming the block is set that way.


If the block is still not visible, the specific user/role may not have the permissions to see whatever content you are trying to view.  Check the permissions for the role at /admin/people/permissions