I think people thought for a long time on how to save the story, and not only the name, from being forgotten. Apple's original logo was designed as a such tribute.
I saw photos of Wozniak ostensibly (?) wearing heart-shaped glasses at the time, that left me with impression the logo could be intentional.
I've read up on this just now and it seems that logo indeed had nothing to do with commemorating Turing's oppression. The rainbow was due to a design trend at the time, Commodore and Atari logos sporting rainbows too.
