MySQL selecciona la longitud máxima de la cadena coincidente

Con un índice en name , lo siguiente debería ser extremadamente eficaz:

SELECT DISTINCT name
FROM   myTable
WHERE  name LIKE CASE
  WHEN NOT EXISTS(SELECT * FROM myTable WHERE name LIKE 'S%') THEN '%'
  WHEN NOT EXISTS(SELECT * FROM myTable WHERE name LIKE 'St%') THEN 'S%'
  WHEN NOT EXISTS(SELECT * FROM myTable WHERE name LIKE 'Sta%') THEN 'St%'
  WHEN NOT EXISTS(SELECT * FROM myTable WHERE name LIKE 'Stac%') THEN 'Sta%'
  WHEN NOT EXISTS(SELECT * FROM myTable WHERE name LIKE 'Stack%') THEN 'Stac%'
  WHEN NOT EXISTS(SELECT * FROM myTable WHERE name LIKE 'StackO%') THEN 'Stack%'
  WHEN NOT EXISTS(SELECT * FROM myTable WHERE name LIKE 'StackOv%') THEN 'StackO%'
  WHEN NOT EXISTS(SELECT * FROM myTable WHERE name LIKE 'StackOve%') THEN 'StackOv%'
  WHEN NOT EXISTS(SELECT * FROM myTable WHERE name LIKE 'StackOver%') THEN 'StackOve%'
  WHEN NOT EXISTS(SELECT * FROM myTable WHERE name LIKE 'StackOverf%') THEN 'StackOver%'
  WHEN NOT EXISTS(SELECT * FROM myTable WHERE name LIKE 'StackOverfl%') THEN 'StackOverf%'
  WHEN NOT EXISTS(SELECT * FROM myTable WHERE name LIKE 'StackOverflo%') THEN 'StackOverfl%'
  WHEN NOT EXISTS(SELECT * FROM myTable WHERE name LIKE 'StackOverflow%') THEN 'StackOverflo%'
  ELSE 'StackOverflow%'
END

Véalo en sqlfiddle .