There are several options here. First, you could use the Django "sites" framework, which has the advantage of being idiomatic and familiar to other Django developers:
http://docs.djangoproject.com/en/dev/ref/contrib/sites/
Second, you could define a database backend per customer (using the Django 1.2 multi-DB support) and write a custom database router that is aware of your custom FastCGI environment variables:
http://docs.djangoproject.com/en/dev/topics/db/multi-db/
Third (and best, IMHO) would be to run separate FastCGI processes for each customer, and route appropriately from Nginx. This approach is obviously the most complex setup, but it has the major advantage of letting you run every customer's FCGI backend under a different user id, offering yet another level of protection against data leakage and other security issues.