The problem is that the assignment isn't parsed as it would be in your source text. The fastest thing to do is to split it:

my $cookie = 'name1,value1,name2,value2';
my %hash = split(',', $cookie);
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Or you can use string eval on your quoted string (but why?):

my $cookie = '("Name1","Value1","Name2","Value2")';
my %hash = eval $cookie;
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update: But don't do that. As crazyinsomniac points out, it's not a really good idea to eval cookie contents...