Rails Undefined Method 'model_name'

Besides the correct route in your config/routes.rb, you will also need these two instructions on your model:

include ActiveModel::Conversion
extend  ActiveModel::Naming

Take a look at this question: form_for without ActiveRecord, form action not updating.

For the route part of these answer, you could add this to your config/routes.rb:

resources :contacts, only: 'create'

This will generate de following route:

contacts POST /contacts(.:format)  contacts#create

Then you can use this action (contacts#create) to handle the form submission.