In a mongo script you can use the db.getSiblingDB('new_db_name') to get a reference of a new database. So, it it not mandatory to give the database name in the command line. You can use the script.js:
db = db.getSiblingDB('new_db_name');
print(db);
// the rest of your code for database "new_db_name"
and the output of this script is (invoked with mongo script.js):
MongoDB shell version: 2.2.2
connecting to: test
sag