Have you checked your Mandrill API logs?
I am having the same issue and noticed that the emails are being sent to the Mandrill API (since I set my smtp settings for Mandrill in settings.py), but that the from_email and from_name are empty in the API calls.
So, I found https://github.com/brack3t/Djrill and am about to install it. I'll let you know if it "just works".
EDIT: So after installing djrill and following the documentation I'm getting failed API calls for error messages - the from_email is showing as "root@localhost" for some reason.
When I do the shell test shown on the github page (with an email from an accepted domain for my Mandrill account replacing Djrill Sender), it works:
from django.core.mail import send_mail
send_mail("It works!", "This will get sent through Mandrill",
"Djrill Sender <djrill@example.com>", ["to@example.com"])
It turns out that I had my default "From" email setting name confused. Its called SERVER_EMAIL. See https://docs.djangoproject.com/en/1.3/ref/settings/#std:setting-SERVER_EMAIL.
So the following in settings.py fixed my issue:
SERVER_EMAIL = myname@myMandrillApprovedDomain.com