Setting a default 'From' address when sending an email from Cases

Hi there this functionality does already exist in salesforce there are two ways to achieve this

1) If you are using Case Feed Layout you can manage this from the page layout.

Edit the page Layout enter the Feed view and "Specify From Address(es)"

2) If you are not you can load the details in against the user

Sender Email and Sender name

Downside of option 2 is you will have to verify each user individually

Hope that helps