$ perl -E 'use File::Basename; say "|$_|" for fileparse("X.tgz", qw{.gz .tgz})'
|X.|
|./|
|tgz|

$ perl -E 'use File::Basename; say "|$_|" for fileparse("X.tgz", qw{\.gz \.tgz})'
|X|
|./|
|.tgz|

##</code><code>##

$ perl -E 'use File::Basename; say "|$_|" for fileparse("X.tar.gz", qw{\.gz \.tgz \.tar\.gz})'
|X.tar|
|./|
|.gz|

$ perl -E 'use File::Basename; say "|$_|" for fileparse("X.tar.gz", qw{\.tgz \.tar\.gz \.gz})'
|X|
|./|
|.tar.gz|

##</code><code>##

substr $filename, rindex($filename, ".") + 1 || length $filename

##</code><code>##

$ perl -E '
    say "oldfile\t ext \tnewfile";
    say "-------\t --- \t-------";

    my $newname = "edddd";

    for (qw{OPQ.RST .U V. .W. X.Y Z . ..}) {
        my $ext = substr $_, rindex($_, ".") + 1 || length;
        say "$_\t|$ext|\t$newname" . (length $ext ? ".$ext" : "");
    }
'
oldfile  ext    newfile
-------  ---    -------
OPQ.RST |RST|   edddd.RST
.U      |U|     edddd.U
V.      ||      edddd
.W.     ||      edddd
X.Y     |Y|     edddd.Y
Z       ||      edddd
.       ||      edddd
..      ||      edddd