Does this include collecting or displaying their real name? Is that considered PII as it pertains to this law? I ask because if I run a forum it will be diffi

Does this include collecting or displaying their real name? Is that considered PII as it pertains to this law? I ask because if I run a forum it will be difficult to force people to use fake names unless I generate names for them. Some people would be upset if I force them to use a randomly generated name, though some would be happy to be anonymous.