Is there some hidden connection or just coincidence that both of the vampires in her life shared the same human name?
I read somewhere that the writers claimed William/Liam was coincidence - I don't believe them. There's also Will(ow) and the connections between her and Spike from midway through S6 to Chosen are immense. Events leading up to his ensoulment twin them. The editing suggests their separate conflicts take place simultaneously despite logical reasons to doubt the chronology. Just as light connects them in Chosen, so dark Willow/dark Warrior connect them here. At one stage, the flame on her hands matches a shot of Spike’s hand in contact with the flaming hand of a demon. Intercutting brings together his attempt to destroy one of two parallel worlds (monster/man) with Dark Willow’s attempts to destroy the world in its entirety. Her actions result from an excess of feeling, His are the result of too little. Both misunderstand the concept of feeling. The fight between Spike and the demon-warriors is shown as synchronic with the fight between Willow and Buffy. Both dispatch their enemies. The connection continues throughout S7 (both have arcs of redemption, have to learn to be trusted and to trust themselves etc.) culminating with the light connection in Chosen.
William is derived from two elements wil = "will or desire" and helm = helmet, protector. It's interesting that Xander's name also means protector or defender - but of men, fitting given his relationship with vampires and somewhat ironic in other ways. As humans both our vampires lived up to their name - William protecting his mother, Liam protecting Kathy. When we're first introduced to them as vampires they're protecting someone.
Vampires as a motif, conceit, metaphor - call it what you will - represent the Id. The Id is the unconscious part of the mind and it contains the basic drives - Eros (which contains the libido), and the aggressive (death) instinct, Thanatos - Love and Hate.* The Id operates according to the pleasure principle - this is what Freud means by sex - pleasure in the general sense not sexual intercourse. The Id wants its drives satisfying - it demands instant gratification. Because it has no sense of self/other, gratification is directed inwards - the Id is narcissistic. Humans are similarly driven by the same instincts (the English term doesn't convey the same meaning as the original German -
triebe) but the drives are mediated by the reality principle - by what society or the Superego will allow.
The fundamental difference between William the Bloody and Angelus is the way each continues to live up to his name. WtB 's desire to protect is made manifest in his relationship with Dru. It's selfish because it's inwardly directed nevertheless it's still there (arguably it was just as narcissistic as a human but that's a different argument). Liam rejects his name and with it his desire to protect anyone but himself. It could be argued that he's driven to protect the group (but this is still narcissistic because he's the leader of the group - it's where his identity derives). Angelus is an ironic inversion that will be inverted again. WtB doesn't change his name until later and I think this is in response to Angelus. In order to survive, William becomes Spike because he needs to hate more. When Angelus becomes Angel he needs to find love.
It seems to me that in both there is a conflation of the drives but the balance is different. With WtB, Eros is manifest - Thanatos is latent. In Angelus it's the other way around. Angelus loves evil, loves death - he takes pleasure in planning evil - Darla perhaps comes second - she's not his focus. William loves love - he gets an adrenaline rush from killing but he takes pleasure in Dru - he loves life. It's why - I think - Spike finds the transition to souled easier. He already has the capacity to love. Angel has to learn it. Another fundamental difference is Spike - souled/unsouled - operates closer to the pleasure principle. Angelus/Angel seems to operate predominantly according to the reality principle - Angelus could plan and had a far greater sense of the other - WtB was impulsive. If Spike is better equipped to love - perhaps Angel is better equipped to live with others. This - I think - is down to the relationships they had with their respective parents. Spike has an absent father; Angel an absent mother. In the first there's an over-identification with love, in the latter an over-identification with the Law.
The above is over simplified. Liam's obvious name changes add a level of complexity just as William's lack of name change does. How the connect works with the other "William" derivatives, I don't know. They don't necessarily connect in the same way as the above and the connection need not symmetrical but they'll be there. I'm with
@dcai0830 in as much as I fear this turning into a battleship but I don't mean to imply that either vamp is better than the other - just point out the similarities and differences in relation to the shared name. It would need a more nuanced analysis to address contradiction.
* (all Caleb needs is the words tattooed on his hands and he is the Pastor from The Night Of The Hunter - I digress but not too far because I think there's a connection between Caleb, Angel and Spike - a "what if" connection).
Apologies for the length - this is the abridged version.
🙁