Akin to PyMongo's MongoClient.get_default_database:

http://api.mongodb.org/python/current/api/pymongo/mongo_client.html?highlight=get_default_database#pymongo.mongo_client.MongoClient.get_default_database

Takes a client and returns a mongoc_database_t if the client was created with a database name in the URI, otherwise returns NULL.

Useful because you can change the database used for operations just by changing a configured URI, without code changes.