Noah is a hard name to pair, IMHO - ideally it needs a name beginning with a strong consonant to follow it, otherwise they all just blur together. Maybe not an issue, if you never really intend to use the full name other than formal occasions.
Having said that, I don't like "Noah Teddy", as I don't like Teddy full stop. Ted, maybe, Edward is better. "Edward Noah" is good, Ted for short?