The father is cloning himself. And not clones in the sense of the Shadow Clone Technique, but actual living duplicates he's growing from birth or a young age, possibly involving the use of White Zetsu. It makes sense to the fact that the father and son share names, that there are multiple sons, that they share the same Sharingan, and that he shares no true familial attachment. Baldy is called "father" because he's the original, and the one that created them. Organ transplant is easy because they have the same bodies. In fact, the multiple implanted Sharingan on the father's body could be possible due to his cloning method, or they're taken from deceased or failed clones so as not to be put to waste.