The File::Basename module does what you need:

use strict;
use File::Basename;

print basename $_
  for <DATA>;
__DATA__
/home/users/me/proteins/1hc9.txt 
/home/users/me/proteins/193l.txt 
/home/users/me/proteins/1trz.txt 
/home/users/me/proteins/2psg.txt
[download]