Any of the premium templates support search. This includes a category filter and a keyword search. The keyword search support many of the core fields. You can see which field on the Connections :: Settings admin page under the Search tab.
This would easily cover the name and department requirements. If you use categories for language and methods you could use an advanced search addon which I sell. You can see it in action on this live production site, the “Find A Therapist” section:
If you are interested in this add on I can provide you with a quote which includes installation and configuration. Please use the Contact link at the very bottom of the page to contact me for the quote.
Hope that helps!