How do I send an email for approvals using a drop down with department names

I suggest the following:

• Add a configuration list to the site, containing department name as well as the department lead as columns.
• Add department name to the list your workflow should run on, but as a lookup field to the configuration list department name column. 
• Open up your workflow:
  • Use the query list action to retrieve the department lead from the configuration list while you filter on department name, store department lead in a variable. Guess you can do it with list lookup to, directly in a variable but I prefer the query list action. 
  • Use the department lead variable in your approval tasks. 

I would avoid the use of the switch statement as I think it adds more complexity to it because all tasks need to be duplicated and managed separately afterwards. Though, if the tasks that you assign to the different department leads all need to be different from each other, use the switch statement.

Goodluck!