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 use JSON::PP;
my $json = JSON::PP->new;
my $json_output=encode_json( { JSON1=> \@my_A } );
print $json_output;

{"JSON1":["{\"name\":\"Name 1\",\"myArray\":[1,2,3]}","{\"name\":\"Nam
+e 2\",\"myArray\":[4,0,0]}","{\"name\":\"Name 3\",\"myArray\":[5,0,6]
+}"]}

{"JSON1":[{"name":"Name 1","myArray":[1,2,3]},{"name":"Name 2","myArra
+y":[4,0,0]},{"name":"Name 3","myArray":[5,0,6]}]}