optimizing SELECT with LIKE

I have 3000000 rows in a database where I have to make a:

SELECT name FROM table WHERE name LIKE '%firstname%' AND name LIKE
'%secondname%';

to obtain the data I need.

Due to the data nature, there is no other way to look for the data, it's old
data that was registered in paper years ago, with no searchable index... just
names, that sometimes are wrote like: JORGE SARMIENTO, other times like:
SARMIENTO, JORGE and other times like JORGE LUIS SARMIENTO. and due to legal
reasons, the data must be entered the exact way it was wroten.

Is there any way to optimize postgres for doing this kind of SELECT?

thanx in advance!

Jorge S.