The novel doesn't indicate that birth-fathers' identites are known as the whole pregnancy and birth process is a laboratory procedure.
I would assume that the whole process of fertilization is handled in the lab through in vitro fertilization. Perhaps the birthmothers are surrogates with no physical relationship to the fetus that they carry.
Depending on one's station in this society, they would select the characteristics that are desirable from various groups in the society.
I think this is a "hole" in the book that leaves plenty of room for speculation on the part of the reader. And, are the birthmothers selected for their good genetic qualities?