Unexpected behavior from ltrim in postgres
The 2nd parameter is the list of characters to trim, not a string as such.
The manual about ltrim(string text [, characters text]):


  Remove the longest string containing only characters from characters
  (a space by default) from the start of string.


So this:

select ltrim('abc cab b ca foo', 'abc ');


... only leaves 'foo'.



To actually remove one leading string 'Test ':

SELECT regexp_replace('Test ThingTest ', '^Test ', '');


But to update a table, this is typically much more efficient:

UPDATE tbl
SET    col = right(col, -5)  --  right(col, length('Test ') * -1)
WHERE  col LIKE 'Test %';


Only touches relevant rows (important!), can use an index where appropriate (important if only few rows in a big table are affected) and the expression is cheaper, too. About that index:


PostgreSQL LIKE query performance variations