(The spelling as Caulfeild was correct at the time.)
Holden begins his story:
If you really want to hear about it, the first thing you’ll probably want to know is where I was born, and what my lousy childhood was like, and how my parents were occupied and all that before they had me, and all that David Copperfield kind of crap, but I don’t feel like going into it.
And David Copperfield does start just as Holden describes it. David says:
I was born with a caul, which was advertised for sale, in the newspapers, at the low price of fifteen guineas.
The start of childbirth is usually announced by the “waters breaking”, that is the amniotic membrane ruptures with the release of amniotic fluid. Very occasionally the membranes don’t rupture, and the neonate is born within the amniotic sac, which had to be opened by the “gossip” or midwife. It was thought that being born in a caul was lucky, preventing death from drowning; sailors used to buy them as a precaution, a lucky charm.
Nowadays, at least in the westernised world, being born in a caul is very rare; if the waters don’t break, the membranes will be ruptured artificially. (The membranes are delivered in the third stage of labour, with the placenta.)
So, if “caul” implies luck, what about “field”? It might be over-thinking things, but perhaps field refers to batting away questions — with the unvoiced idea that the questions aren’t answered. Perhaps. If so, Caulfield is a cratylic.