How to set up test db settings in a DRF project?

I'm running unit tests in a drf project with a mongo db and djongo connector. When I run tests one by one they compile successfully but when I run all of them with python3 manage.py test test.path they all fail except the first test. The following line from the logs indicates that there is an issue with dropping the test database.

FAILED SQL: DROP DATABASE "test_my_project_name"

Here's the database configuration.

DATABASES = {
    'default': {
        'ENGINE': 'djongo',
        'NAME': 'my_project_name',
        'CLIENT': {
           'host': os.environ[DB_HOST],
        }
    },
    'test': {
        'ENGINE': 'django.db.backends.postgresql',
        'NAME': 'test_mytestdatabase',
        'USER': 'mytestdatabaseuser',
        'PASSWORD': 'mytestpassword',
        'HOST': 'localhost',
        'PORT': '5432',
    }
}

What do I need to do to make the test db be used during tests and not the main db.
Also do I need to set up anything else for the testing?

During tests django use default config. Only difference is that before and after each test, it creates and destroys test db named after your default db with test_ prefix.
Your error confirms that by saying it cannot drop test_my_project_name database - your default db name is my_project_name while your "test" db name is test_mytestdatabase.

You'll have to use different approach explained in this SO answer.

In short, you must use entirely different DATABASES config for testing:

import sys
if 'test' in sys.argv:
    DATABASES['default'] = {
        'ENGINE': 'django.db.backends.sqlite3',
        'NAME': 'mydatabase'
    }

I would suggest storing that condition as one of the settings variables, for example

TEST_MODE = 'test' in sys.argv

and then you can use it for many things in runtime (logging, stubs, skip some validation, etc...)