Draft Day has no accounts and asks for no email address. What it stores is what a commissioner types in: a league name, a list of manager names, candidate dates, and the hours each manager marks as free.
Manager names come from whoever set the poll up. If your name is on a poll and you'd rather it weren't, ask your commissioner to remove it — they can edit the roster or delete the whole poll, answers included, from the poll settings.
Anyone with the link can see the poll and everyone's availability. That's the point of it, but it means these links are effectively public. Don't put anything in a league name or note you wouldn't want forwarded.
Availability data is kept so the poll keeps working. Nothing is sold, and there are no advertising trackers. Traffic is measured in aggregate — page views and load times — with no profile built about you.
Questions, or want a poll removed and you can't reach the commissioner? Get in touch and it'll be deleted.