I work with customers in the US and am asleep during most of their work hours. In general customers should know when they can and can't get ahold of you.
You don't need to mention you are a night owl, but you should set expectations regarding your availability. For example, "My office hours are from 11am to 9pm" is fine.
I wouldn't mention your waking cycle. There could be all kinds of reasons for keeping non-traditional working hours.
One of the huge considerations though is ensuring there is some overlap with their work cycle. You want to ensure you are available to talk and there may be cases when you may want to get up early. But as long as you are clear about how to get in contact with you and you can be reliably contacted, I don't see a problem.