When travelling outside of the United States or Canada, the name on your travel documents must match the name on your passport. You should sign up using your full legal name.
Once you're signed up on the trip, make sure to enter your passport information on My Profile under the 'Traveler' section.
The deadline to update passport information is 30 days prior to your final balance date.
If you've signed up with a nickname, not to worry! As long as your passport information is filled out and correct, you're travel documents will have your legal name!