There are many reasons to rename a Mongo Database. This should be done with caution - and backups are advised before performing any database operations.
Note: You must have Mongo 2.6 or later installed.
Database Copy method
First, connect to MongoDB's shell.
mongo
Next, copy the old content to the new database.
use old_database
db.copyDatabase('old_database', 'new_database')
Verify the new database has been copied.
use new_database db.collection.count()
Now the old database can be removed
use old_database db.dropDatabase()
Rename using Backup/Restore
Before using the mongo shell, use the mongodump and mongorestore commands. You may have to be an admin/root to do this.
mongodump old_database mongorestore --db new_database ./dump/old_database
Then, connect to MongoDB's shell.
mongo
Verify the new database has been copied.
use new_database db.collection.count()
Now the old database can be removed
use old_database db.dropDatabase()