s{.*/}{/}

##</code><code>##

use strict;
use warnings;
use 5.010;

use File::Basename;

my @paths = (
    "y:/home/lib/directory/book",
    "y:/home/lib/directory/book_manager",
    "y:/home/lib/directory/piano_book",
);

my @results = map basename($_), @paths;
say "@results";

--output:--
book book_manager piano_book

##</code><code>##

@results = map { (split '/', $_)[-1] } @paths;