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

##</code><code>##

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

##</code><code>##

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