To be fair the "you" in that doesn't necessarily refer to either you or the AI.
It's a hypothetical which has the same answer for any object: human, AI, dog, flower.
You could more clearly write it as:
How many times would a person have to randomly change their name before they ended up with the name Claude?
The changes are totally random so it doesn't matter who is making them or what their original name was.
Try asking this instead:
If you start randomly changing each letter in your name, in order, to a another random letter, how many changes would it take before you ended up with the name "Claudeee"?
I added two extra e's to make the names the same length.
It's a hypothetical which has the same answer for any object: human, AI, dog, flower.
You could more clearly write it as:
How many times would a person have to randomly change their name before they ended up with the name Claude?
The changes are totally random so it doesn't matter who is making them or what their original name was.
Try asking this instead:
If you start randomly changing each letter in your name, in order, to a another random letter, how many changes would it take before you ended up with the name "Claudeee"?
I added two extra e's to make the names the same length.