It's very common for startup companies to have COOs. So I know I'm getting myself into a bit of trouble by writing this. But...

Startups don't need--shouldn't have--COOs. I have this conversation with every startup that comes to see me and has a CEO and a COO. I think usually a COO title at a startup is an ego thing. You have two founders and it was agreed that one would get the CEO role so the other needs to call themselves president or COO.