Update: As AnomalousMonk mentions below, I should have kept the original to remind me to read carefully before hitting submit ;)

So, here's the code I originally posted, using lazy to set the attribute based on information the class learns after it's created:

has FileName => (
    is => 'ro',
    isa => 'Str',
    lazy => 1,
    builder => '_build_filename',
);

sub _build_filename {
    my $self = shift;
    # build logic here
    return $filename;
}
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