Since the name is carried by the males (traditionally) then how could the Howard females (who are not related at all to each other) share common traits (e.g. My wife is not related to my mother, herself not related to my paternal grandmother, the paternal line is the one that carries the family name)? This is a major oversight!
Not as major as it might appear.
Generally, people worry about the concept of "the Howard women" mentioned several times in the episode. Why would "the Howard women" refer to a long line of women all named Howard? It never does in everyday life. Rather, it refers to the women in the family line of the Howards, as opposed to the family line of the Crushers, from the POV of Beverly Crusher née Howard. Beverly just needs to distinguish between the Howards/the Howard women and the Crushers/the Crusher women here, and the Ghost adopts her vocabulary for its nefarious purposes, while Picard echoes it for quite the opposite reason. So this is not a problem at all.
The
actual problem is more specific and concrete: the Ghost referring to a woman explicitly
named Howard, who is not Beverly's mother but a woman from 800 years back - one Jessel Howard, the Ghost's supposed first "love"/victim!
Here we'd have to believe in a strange coincidence indeed. Why does the Ghost meet its final fate when randomly encountering (the daughter of) another woman who happens to be named Howard? We could argue the Ghost likes the name. But then it becomes the coincidence of it meeting a Howard who happens to be related to the original Howard.
But is that a coincidence - or is it a quest? In the 24th century, the Ghost has more freedom of movement than ever before, and access to vast databases. It could have homed in on Felicia Howard quite on purpose, for old times' sake. And the very circumstances that facilitated the reunion with a Howard named Howard would bring down the Ghost, as the world would have outpaced its methods of self-preservation, and the vast databases would defeat ignorance and superstition.
The secondary problem here is Crusher's casual reference to something called "the Howard clan" at one point. We may take that to mean there was a clan of that name, in which case it having anything to do with Jessel Howard would be a strange coincidence indeed. Or then we may insist it's Beverly's way of saying "my mother's Clan" as opposed to "my father's Clan" (assuming Crushers were Scots, too) or, say, "my uncle's Clan" (a putative major influence in her life, and the cause for a need to distinguish).
The tertiary problem is the green eyes thing: if it runs in the "Howard women" bloodline, which in the realistic model never met the Ghost between Jessel and Felicia, it can't be the doing of the Ghost. But nothing says it would need to be. It's just a green herring, a species commonly found in all ghost stories...
(And no, this has got nothing to do with writer intent. But it isn't supposed to.)
Timo Saloniemi