With a big caveat (as you indicated re: Amalek) that not all names found in Tanach and Shas are necessarily appropriate for baby naming. It would be hard to imagine naming a boy בלעם or a girl איזבל in good conscience (although wouldn't be surprised if it's been done)!
Tanach
While some names are used by more than one person, for sheer numbers I have counted over 1600 named male individuals in Tanach and over 125 named females.
There is an excellent comprehensive and indexed name list here (in Hebrew) with name explanations.
There's also a very good list of male names here and female names here and I actually used this for much of the person data in my site's 3D Tanach Family Tree feature. If you're into genealogy, they even have a GEDCOM formatted file with family tree info included for download here.
In Mandelkern's Concordance of the Tanach there's a section at the end with a listing of named items (people, nations, places, H's name). While this is not limited to person names, it's also a valuable resource for this discussion.
If you want to actually search for any mentions of male and/or female names in Tanach you can do the following on my aforementioned site:
1) select a letter-based search from the search settings panel on the right
2) enter an asterisk as a wildcard to search for any word
3) select Advanced search from the control to the right of the search bar
4) select the Parts of Speech++ tab
5) select one or two name settings from the Objects list (can be MAN and/or WOMAN)
6) click the search button on the left side of the search bar
7) see the search results (in this case for woman name) with the names highlighted in red for each pasuk where they occur.
Shas
A comprehensive list of male and female names in Shas can be found in
תולדות תנאים ואמוראים, אהרן הימן, תר"ע
and much of it has been digitized and indexed here.
