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.