use strict;
use warnings;

my $namesFileName = shift;   # Get name of the file names file from command line

open my $inNames, '<', $namesFileName or die "Unable to open $namesFileName: $!\n";

while (<$inNames>) {
    chomp; # Remove line end character from file name
    open my $dsspIn, '<', $_ or die "Unable to open $_: $!\n";
    ...
}

close $inNames;