Trovare un genitore di primo livello in SQL

Puoi utilizzare CTE ricorsivo per ottenere ciò:

DECLARE @childID INT 
SET @childID  = 1 --chield to search

;WITH RCTE AS
(
    SELECT *, 1 AS Lvl FROM RelationHierarchy 
    WHERE ChildID = @childID

    UNION ALL

    SELECT rh.*, Lvl+1 AS Lvl FROM dbo.RelationHierarchy rh
    INNER JOIN RCTE rc ON rh.CHildId = rc.ParentId
)
SELECT TOP 1 id, Name
FROM RCTE r
inner JOIN dbo.Person p ON p.id = r.ParentId
ORDER BY lvl DESC

DEMO SQLFiddle

MODIFICA - per richiesta aggiornata per genitori di primo livello per tutti i bambini:

;WITH RCTE AS
(
    SELECT  ParentId, ChildId, 1 AS Lvl FROM RelationHierarchy 

    UNION ALL

    SELECT rh.ParentId, rc.ChildId, Lvl+1 AS Lvl 
    FROM dbo.RelationHierarchy rh
    INNER JOIN RCTE rc ON rh.ChildId = rc.ParentId
)
,CTE_RN AS 
(
    SELECT *, ROW_NUMBER() OVER (PARTITION BY r.ChildID ORDER BY r.Lvl DESC) RN
    FROM RCTE r

)
SELECT r.ChildId, pc.Name AS ChildName, r.ParentId, pp.Name AS ParentName
FROM CTE_RN r
INNER JOIN dbo.Person pp ON pp.id = r.ParentId
INNER JOIN dbo.Person pc ON pc.id = r.ChildId
WHERE RN =1

DEMO SQLFiddle

EDIT2 - per fare in modo che tutte le persone cambino UNISCI un po' alla fine:

SELECT pc.Id AS ChildID, pc.Name AS ChildName, r.ParentId, pp.Name AS ParentName
FROM dbo.Person pc 
LEFT JOIN CTE_RN r ON pc.id = r.CHildId AND  RN =1
LEFT JOIN dbo.Person pp ON pp.id = r.ParentId

DIMOSTRAZIONE SQLFiddle