Yes, a name is strictly speaking unnecessary, but you need to actually identify a real person uniquely in the real world.

its not PII as long as its impossible to link it back to a unique identification from the real world such as a name, social security number or similar.

so my previous blanket statement of IP addresses not being PII is slightly exaggerated, they can be, but they rarely are.

most people access the internet either with dynamic ip addresses or from a corporations internet providers. people that have a static ip address on a private landline and without a NAT are rare, which is why generally speaking, IP addresses aren't PII.

it does become PII if the person in question has a static ip address and is the only person using this connection.