why wouldn't the name=>"Accounts" be picked up

In your original data the first element of the array is unwanted so toolic has @{ $data }[1 .. $#$data] which has the effect of skipping that first element. Arrays are indexed from "0" so the first element is $array[0], the second element is $array[1] and so on. So, @{ $data }[1 .. $#$data] means the range of elements starting at the second element and up to the last element.

A better way might be to use grep in combination with map:

my @all_names =
    map { {name => $_->{name}} }
    grep { exists $_->{name} }
    @$data;
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Here grep first filters all the elements, discarding any which don't have a 'name' key, and then map constructs the desired data structure from the remaining elements.