All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
Islam forbade us from being traced back to other than our real father and we have already discussed this in Fataawa 133682 and 82371.
Therefore, in principle it is forbidden to trace back those two daughters to other than their real father. However, if there is a preponderant benefit, like repelling a definite harm or what is predominantly thought to be a harm which necessitates tracing back each of the two daughters to other than her real father, then she should be given an indefinite father's name, i.e. without intending to trace her back to a particular person, while preserving her real lineage by having witnesses on it, for instance.
In any case, a Muslim should be intelligent and wise so that he would not subject himself to being questioned by the authorities about this matter. Sa’d ibn Abi Waqqaas said that the Prophet said: "Beware of matters that make you seek excuses.” [Al-Bayhaqi and Al-Haakim who graded it Saheeh (sound)]
Allaah Knows best.