This works:

@files = ("one.zip","twotwo.doc","three3.ppt","testfour");
map {$_ =~ /([^.]*)\.?/; push (@onlyNames, $1); push (@onlyExt, $');} 
+@files;
[download]

Consider the following input, which will cause a complete path instead of a filename to be pushed into your @onlyNames array:

/usr/bin/perl
/home/users/d/davido/text.txt
C:\Perl\scripts\mytest.pl
[download]

In each of those cases, you'll capture into @onlyNames the following:

/usr/bin/perl
/home/users/d/davido/text
C:\Perl\scripts\mytest
[download]

It gets even worse if one of the directory names in the path contains a dot (.)

Consider what happens if the input looks like this:

C:\Perl\scripts.old\mytest.pl
[download]

In that case, @onlyNames will contain:

C:\Perl\scripts
[download]

And clearly that's not a filename.

Update: Just thought of another situation that may reveal a bug: What if the filename has multiple extensions? In this case, it would be up to the OP to define what constitutes an extension, and what constitutes a filename. But by way of example, your solution would turn:

bigfile.tar.gz
[download]

...into...

bigfile
[download]

The danger here is that while .gz represents the extension, .tar represents a second layer of 'extension'. But the name of the .gz file really is bigfile.tar, since we're dealing with multiple layers of processing on the said file.