If you uploaded the wrong file into the database via cpanel, such as dbname_2013.zip, chances that the name will appear in your database even though you have pressed the "Delete Database" link.
If you go to mysql, you would not see the database also.
To remove, this is an example of it.
# cat /var/cpanel/databases/studidib.yaml
The one that gave problem is studidb_2010sql.zip.
You may go to "/var/lib/mysql" folder to remove it, but it's possibly that the database may not be there.
As such, modify the file "/var/cpanel/databases/studidib.yaml " and then remove the line "studidb_2010sql.zip" and then remove the /var/cpanel/databases/studidb.cache file.
After that, run this command : /scripts/update_db_cache