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foreach (@files)
{
...
      $_ = map m{([^/]+)\.txt}, $_;  #Strip out of the string the path
+ and extension leaving only the filename intact
      ...
}

( my $name ) = m{ ([^/]+) \.suffix }x;

...

use File::Basename;
my $name = fileparse( $_ , qr{ \.suffix }x );