For your first two cases the solution is straight forward, but you need to do a bit more to cover the third. Here is one way, maybe not so efficient but something to build on. I am assuming your focus is on the artists - i.e. you want to rank each artist as opposed to ranking each line.

use Data::Dumper;
$Data::Dumper::Sortkeys = 1;

my %artists = (
    'William Blake' => 1,
    'David Hockney' => 1,
    'Francis Blake' => 1,
    'David Lynch' => 1,
);

my @lines = (
    'William Blake',
    'Blake Morrison',
    'david lynch',
    'francis bacon',
    'William Blake and Blake Morrison',
);

my %rank;

# make artists lower-case for case-insensitive match
my %artists_lc = map { lc($_) => $_ } keys %artists;

# map all the artist words
my %artist_words;
for my $artist ( keys %artists ) {
    my @words = split( /\s+/, $artist );
    for my $word ( @words ) {
        $artist_words{lc($word)}{$artist}++;
    }
}
# have a look at the map
print Dumper(\%artist_words);

for my $i ( 0 .. $#lines ) {
    my $line = $lines[$i];
    my $artist;
    my @words = split( /\s+/, lc($line) );
    for my $word ( @words ) {
        if ( my $hash = $artist_words{$word} ) {
            $rank{$_}{$i}++ for keys %$hash;
        }
    }
    # deal with exact and case-insensitive
    if ( $artists{$line} ) {
        $rank{$line}{$i} = 256;
    }
    elsif ( $artist = $artists_lc{lc($line)} ) {
        $rank{$artist}{$i} = 128;
    }
}

print Dumper(\%rank);
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Output:

{
    Artist => {
        line_index => score
}

{
    'David Hockney' => {
        '2' => 1
    },
    'David Lynch' => {
        '2' => 128
    },
    'Francis Blake' => {
        '0' => 1,
        '1' => 1,
        '3' => 1,
        '4' => 2
    },
    'William Blake' => {
        '0' => 256,
        '1' => 1,
        '4' => 3
    }
};
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