By looking at the code, not clear why you need .map, it doesn't look like the code is trying to alter the object persona. it simply get the result from API and bind to the dropdown. Anyway, something like below should work. Refer below link for an example.
$.map( result.data, function( value, key ) {
$scope.dropDownListManager.add({
text: key,
value: value
});
});
jQuery.map() | jQuery API Documentation[
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Example:
populate dropdown Example[
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