There's no specific requirement to use named chains. The only ones that iptables specifically cares about are OUTPUT, INPUT and FORWARD. That said, named chains can be very useful for "limiting damage" when you have multiple people administering a host. Instead of having everyone fiddling with INPUT, you can do jumpouts to named-chains and tell people, "make your changes in this chain".

Typically, I place my core rules in INPUT and my application rules into named-chains. The jumpouts to the other chains come after the core rules in INPUT. If I find someone's added further rules directly to INPUT, they typically get summarily deleted.