@ Nancy
I think Connections gets 2 of these…
By topic, I would say yes, using the categories.
By name, yes. The keyword search will search the name fields. To see if the results will meet your needs. Enter a few test entries and on the Connections : Manage admin page you can test the search.
By region, no. The closest is the list can be filtered by region. If you go to the Connections : Settings admin page and add a check to the Region option under the Links section this will make the state part of addresses in the list clickable. When a user clicks on that link, the results will be filtered by the state clicked. This can also be done with the city and the zipcode.
Oh, for the category search and keyword search features, you will need one of the premium templates that has those features available.
I hope that helps and answers you questions thoroughly.