Two things here:
1. Accounts usually have two names they can be identified by, the In-Game Name, which is the name the shows up in-game under your ship, and the Login Username, which is the username you use to login to darkorbit. So if it's your account, you should already know the Login Username, because that never changes.
2. If you are going to contact support to get them to help you recover the account, all you need is the UserID. The Login Username would also help but I'm sure they can identify the account just by the UserID.
You will also have to prove the account is yours, so be prepared to provide payment information, and past information like, passwords from before, emails from before, etc.
A Transaction ID I think would also help a lot for recovery and identifying if your are actually the owner.