You may use a CROSS APPLY

DECLARE @json NVARCHAR(MAX) = '{ "SearchParameters": [ { "LastName": "Smith" }, { "Org": "AAA" }, { "Postcode": "SW1" } ] }';

SELECT k.[key] AS ParameterName, k.value AS ParameterValue
FROM OPENJSON(@json, '$.SearchParameters') AS p
CROSS APPLY OPENJSON(p.value) AS k;