As shown from the Snicket family tree, F. is the child of Chas. Snicket, and the (presumably youngest, seeing as their name is listed last both on the tree an alphabetically) sibling of D. Snicket- the parent of G, H, and I- and E. Snicket- the mother of Jacques, Kit and Lemony. This would make Beatrice Baudelaire II their grandniece.
O could stand for Olaf, who could be a Montgomery sibling. Olaf's tendency towards wicked deeds could explain the noose hanging from the O branch; however, there is no canon indication that Olaf and Monty are directly related in any way, and it is unlikely that Olaf is such a close relative of the Snickets, considering his romantic relationship with Kit.
A plausible theory is that M and O are Miranda and Olivia Caliban, who are somehow closely related and usually theorized to be sisters, and as many VFD families are interconnected, it would make sense that the Snickets and Calibans were related. This is presumably not the case in Netflix canon, however, as Jacques and Olivia are given a romantic relationship; however, this could still be the case in book canon. If this is true, that would make Friday Caliban, Miranda's daughter, F's granddaughter. This would also mean that F is a member of the Caliban family.
The identity of N is not answered by either theory, though some theorize it could be Vice Principal Nero, who works at Prufrock Preparatory School, which is (implicitly in book canon, canonically in the TV series) connected to VFD. Nero could fit into the Caliban theory, considering that all three names are connected to Italy.
|A. Snicket||B. Snicket||Chas. Snicket|
|D. Snicket||E. Snicket †||Jacob Snicket †||F. Snicket|
|G. Snicket||H. Snicket||I. Snicket||Jacques Snicket †||Kit Snicket †||Lemony Snicket||M. Snicket||N. Snicket||O. Snicket|
|Beatrice Baudelaire II|