On Windows from a command prompt, just typing test.pdf will open that PDF is the default viewer.

I don't have a PDF with destinations to try it - or at least I don't think I have. But have you tried ensuring that your PDF destinations actually work?

test.pdf#nameddest=DestinationX at the command prompt?

If that works, I would then try opening the PDF in PDF::API2 including the full path

use strict;
use warnings;

use PDF::API2;

my $pdf = PDF::API2->open("test.pdf#nameddest=DestinationX");
print $pdf->to_string;
[download]

UPDATE - sorry misread, the question - you want to add a destination, not read one!

I've just tried in my PDF editing software and the destination it creates does not appear to be named. The way I had to name it was to associate the destination with a Bookmark which does have a name. I don't know enough about PDFs to know if it is possible for the underlying destination to be named but associating it with a Bookmark seems to have the effect you are look for.