I haven't been as active on the forum recently cause I got auto-logged out but
to go to the topic at hand....
The issue is they're all the same save.
And.
You're saving wrong.
When you start, with absolutely no saves, and click save in game, you'll see a square for that current save, right?
This isn't a save.
This is "New save slot" with all the information attached to it for the current game/save
if you click "New save slot" - it will make a new save, regardless of what you name it.
The only way to truly overwrite the previous "new save", is to (well first create one and then) scroll down the list, until you find the one you actually created - If you only have 1 real save, It will be the bottom slot, while new save slot will be the top slot.
As for changing that save-slots name afterwards.... mmm... I dunno I think that would probably act like new save slot, hard to say.