No real need for dbo.DelimitedSplit8K here if you only expect maximum two parts (left and right). The following will work a bit faster (please note extended sample data):

IF OBJECT_ID('tempdb..#TempTable') IS NOT NULL

DROP TABLE #TempTable

CREATE TABLE #TempTable (

[ID] INT IDENTITY(1,1) NOT NULL,

[DString] NVARCHAR(255) NULL,

PRIMARY KEY (ID))

INSERT INTO #TempTable

SELECT '0111~Apple' UNION ALL

SELECT '02222~Banana' UNION ALL

SELECT '033333~Carrot' UNION ALL

SELECT '044444~Danish' UNION ALL

SELECT '0555555~Eclair' UNION ALL

SELECT '000 NO TILDA' UNION ALL

SELECT NULL

SELECT

ID

,DString

,LEFT(DString, tld.ix - 1) AS

,SUBSTRING(DString, tld.ix + 1, 8000) AS

FROM

#TempTable AS tt

CROSS APPLY (SELECT NULLIF(CHARINDEX('~',tt.DString),0)) tld(ix)