The Japanese title (which translates into "Natsume's Book of Friends"), does not only refer to the book of names, but to the story itself; the story, originally told in books, is full of all the new friends that Natsume makes. —Minkette
Correct me if I'm wrong but I notice that Nyanko-sensei rarely calls people by their real name (the only ones being youkai he knows, Natsume and Reiko). Specifically, he rarely calls any humans by their real names (usually he gives out a nickname or combines their name with a nickname). At first, I thought that has to do with his personality being superior and all that but then I soon realize: to him, human lives are quite fleeting. Really, for him, there would be no point of learning their names because knows that their lives will end soon before he knows. He can trust youkai to generally live long. With Natsume, he might feel like he is reliving his time with Reiko more or less (since I doubt he called her "Reiko" when she was alive, switching that name to Takashi).
Took a long time for this to sink in this troper but finally noticed that there is a large amount of missing moms in this series, especially dead ones (confirmed dead mothers: Natsume's, Natsume's mother Reiko, Natori's, Tanuma's). All their mothers have given birth to those who have some or a lot of spiritual power (with the case of Reiko and her child, while Natsume's mom may or may not have some spiritual, she probably at least had some sort of gene that was transferred and became active in Natsume when he was born). While the childbirth itself may not be the direct cause of death (since Natori still remembers his mother when he was young), it might cause a considerable strain on the body which may cause the mother to die sometime close to the time their child is born. Fortunately, this might not be the case since the cause of death is unknown yet or unconfirmed but if it is, well, it has some Unfortunate Implications.
Chapter 44 confirms that Natsume's mother died right after Natsume was born. Not looking good.
Certain youkai tend to chase after people like Natsume because he would be a very delicious human to eat. While they are after people who are likely capable of fighting back, there are also incidents where this not the case. In Nishimura's special chapter, there was one youkai who chased after Nishimura despite not having strong powers himself. There is also Taki's case where she almost lost 13, probably close, people and herself to a youkai she can't see without the circle (not to mention the said youkai enjoys watching people suffer, meaning this might not be the first time he's done this). Even Natsume was just saved from becoming a youkai's pet only because the Fujiwaras motivated him to fight back. Makes you wonder exactly how many missing children cases are from encounters like this (especially considering most people are not even aware or have a person like Natsume or exorcist in close proximity)?