This is an interesting question for which there are a number of answers
Firstly Service Desk does not support 'multi tenancy' or equivalent methodologies that enable multiple service management systems to be implemented with ease within the one system framework (Unlike many of the main Service desk tools). You have a couple of choices though.
1) Write a Finance Service reqest system in Workflow, possibly using the templates that are available. If you look in the video section for servicedesk videos there is an excellent set of 4 videas by Jason Short taking you through how to do this. (in fact there are some excellent how to videos for Servicedesk there)
2) Make changes to the IT Servicedesk to shoehorn in what is needed
- Multiple email boxes. there is a workflow on Connect here that will enable to set up monitoring of multiple emails inboxes so you can have itservicedesk@ mailbox and a finance@ mailbox
https://www-secure.symantec.com/connect/articles/expanding-servicedesk-75-part-1-monitoring-multiple-emails-single-email-monitor-application .
- There is documentation on connect here about how you can add additional data fields to database to support additional requirements like suporting fields for finance
https://www-secure.symantec.com/connect/articles/how-add-custom-data-existing-processes-incident-management-change-management-etc
- If you use the techician and end user incident looging workflows then you might be best copying these and editing copies to create a specific Finance related call logging. these can use the additional fields you have added to the database
- Within the rules you can ensure routing and other values are set for finance (for example SLA's removed)
- You can edit the edit incident workflow (or copy and edit) and then add the additional data fields you have created for Finance so they can record these
- What you can't do is change the work incident workflow (i.e. the one that is used to close the ticket). This is fixed and IT orientated (so you may need to add a category called finance).
- You can also configure a specific application profile (like the service desk one) which contains the lists for the drop downs and other settings you want to make. There is an article on this on Connect I just can;t find it. The advantage you have with this is you are not hard coding these but adding them to the database so they will always be there post upgrade.
- You will probably want to be careful with security as in my experience Finance don't like the idea of too many people being able to see requests sent to them
I recently implemented SD and added a set of additional data fields in the forms that are context sensitive. i.e. they only appear when certain things are chosen in other fields. Its not easy but its not taht complex.
Hope this helps
Steve