jq - How do I print a parent value of an object when I am already deep into the object's children?

For a more generic approach, save the value of the "parent" element at the detail level you want, then pipe it at the end of your filter:

jq '. as $parent | .details.name | select(. == "James Brown") | $parent'

Of course, for the trivial case you expose, you could omit this entirely:

jq 'select(.details.name == "James Brown")'

Also, consider that if your selecting filters return many matches for a single parent object, you will receive a copy of the parent object for each match. You may wish to make sure your select filters only return one element at the parent level by wrapping all matches below parent level into an array, or to deduplicate the final result with unique.

Give this a shot:

echo $jsonVariable | jq '{Name: .details.name, Id: .Id}  | select(.name == "James Brown")'