-- Sample Data
DECLARE @MyTable TABLE(Name VARCHAR(50), LinkID INT, IsPrimary BIT, ID CHAR(1))
INSERT @MyTable
SELECT 'John Smith', 1234, 1, NULL 
UNION ALL SELECT 'Joan Smith', 1234, 0, NULL
UNION ALL SELECT 'Tom Smith', 1234, 0, NULL
UNION ALL SELECT 'Frank Smith', 9234, 0, NULL
UNION ALL SELECT 'Bob Smith', 9234, 1, NULL

-- Run Upadate
UPDATE
	T
SET
	ID = CHAR(64 + RowNum) 
FROM
	(
		SELECT
			ID,
			ROW_NUMBER() OVER (PARTITION BY LinkID ORDER BY IsPrimary DESC, Name) AS RowNum
		FROM
			@MyTable AS M
	) AS T

-- Check update
SELECT *
FROM @MyTable