The name 'Orry'?

You figured out the right answer yourself. The Mains were descendants of a French duke, who had to flee to America just to escape religious prosecutions in 17th Century France (he happened to be a Hugenotte at a time, when the king of France wanted all his subjects to be Catholic). So there would be some French touches in the Main family, and "Orry" was their version of "Henri" or "Harry".

Intelligence and purity.

The only other thing I found was this:

"Orry as a name for boys has its root in Latin, and the meaning of Orry is "golden". Orry is an alternate spelling of Orel (Latin): from "aurus"."

But if the explanation in the post above is in the book (which I've sadly not read yet, but I should), then that's the canon one.

I haven't read the book but I wondered about this too, and the only thing I can come up with is, maybe it's short for Orville?