Not quite. I don't disagree that they were from the start supposed to be from the same individual, nor that 'Santa Claus' was meant to show Harry they were the same individual. It's just that the first letter was not signed 'Santa Claus' and Harry says it was. This is a mistake on either Harry's or Eliezer's part, (with a lesser hypothesis being that the inaccuracy was a deliberate minor ploy on Harry's part - but that's a bit unlikely and silly)
Maybe he states them as both being signed 'Santa Claus' just because it's simpler to do so. After all, in Harry's mind the author of each note is very likely the same person, so the two notes may as well have both been signed 'Santa Claus'. It potentially saves the time of having to explain (what is to him) a foregone conclusion. Whether or not that's a detail Harry would normally skip is up to you I guess.
Of course it could just be an authorial mistake. But I'm willing to give Eliezer the benefit of the doubt on a minor point like this.
EDIT: New discussion thread here.
This is a new thread to discuss Eliezer Yudkowsky's Harry Potter and the Methods of Rationality and anything related to it. With two chapters recently the previous thread has very quickly reached 500 comments. The latest chapter as of 17th March 2012 is Ch. 79.
There is now a site dedicated to the story at hpmor.com, which is now the place to go to find the authors notes and all sorts of other goodies. AdeleneDawner has kept an archive of Author's Notes. (This goes up to the notes for chapter 76, and is now not updating. The authors notes from chapter 77 onwards are on hpmor.com.)
The first 5 discussion threads are on the main page under the harry_potter tag. Threads 6 and on (including this one) are in the discussion section using its separate tag system. Also: one, two, three, four, five, six, seven, eight, nine, ten.
As a reminder, it's often useful to start your comment by indicating which chapter you are commenting on.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: