I think you're better off avoiding cursors where possible! It's much slower than a straight up statement, such as:
SELECT name,
substring(name,1,charindex(' ', actor_name)-1) FirstName,
substring(name,charindex(' ', actor_name)+1,len(actor_name)) LastName
FROM actors
to do an update, you could do:
UPDATE actors
SET first_name = substring(name,1,charindex(' ', actor_name)-1),
last_name = substring(name,charindex(' ', actor_name)+1,len(actor_name))