Sounds like you're stuck on old-style global file handles (open FOO, ...). This forces you to maintain an array of file handle names to avoid collisions, since you can only have one file handle of a given name. If you're already using lexical file handles, disregard the rest of this post!

Use lexical file handles instead (in general, this is preferred; there is zero advantage to using the other style, and even if the only thing you get from lexical file handles is lexical scope, that's a net win):

my %filehandle_of;
foreach my $filename (@filenames) {

    # here $filehandle is a reference to a new anonymous filehandle in
+ each iteration, you can push it into an array if you don't need the 
+mapping instead
    if (open my $filehandle, '<', $filename) {

        $filehandle_of{$filename} = $filehandle;

    } else {

        warn "could not open '$filename' for reading: $!\n";
        next;

    }

}
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See also perldoc -f open.