I have in my User Profile, one field to define the Database name, that user can connect.
DATABASES = {
    'app_data': {
        'NAME': 'app_data',
        'ENGINE': 'django.db.backends.postgresql_psycopg2',
        'USER': 'postgres_user',
        'PASSWORD': 's3krit'
    },
    'DBNAME_1': {
        'NAME': 'user_data',
        'ENGINE': 'django.db.backends.mysql',
        'USER': 'mysql_user',
        'PASSWORD': 'priv4te'
    }
}
class UserProfile(models.Model):
    user = models.OneToOneField(User)
    dbname = models.CharField(u'Database name', max_length=100, null=True, blank=True)
not connecting to 2 different database only creating in single database
 
     
    