The paternal name question (your father’s last name) on the GOES application should be entered as your current last name or simply, what your passport shows as your last name. For the maternal name (mother’s name) Feel free to leave that question blank as it seems to only apply to cultures that may use both parents last names. Surprisingly enough when I contacted the CBP helpdesk the other day I asked them what their number one question is, and from what I was told it is in regards to the registration question regarding paternal/ maternal last names.