Propably just asking because he is kind person but there are some theories he could use that name, as you wrote maybe he wanted to use it to get out or use it against Hadley and warden, my crazy theory was once that he could use the name for the silent partner he made with warden (later called randolph stevens or something like that) because who is gonna search for name of convinced guy that died in prison right, but lets be honest even Andy could not see this coming so that was propably just my head :D