How would I send emails to my rails app through different email addresses?

How would I send emails to my rails app through different email addresses?

So, I am cloning Gmail for practice with Rails and Backbone.js.
I could send emails out from my rails app, but I can't find any way to
send emails to my rails app. I want people to be able to send an email to
nick@gmaily.com, and david@gmaily.com (where gmaily is my clone name).
I've looked at different services like Cloudmailin, but those seem to only
have one portal into my application, that is one email address to send to,
which my app will receive. I have my app on heroku, but can't seem to find
any solutions in this regard. Any suggestions?
Note: nick@gmaily.com and david@gmaily.com are examples. It could be
nick@whatever.herokuapp.com and david@whatever.herokuapp.com, which is
what I'm actually going for.