There is zero reason to make a distinction between the illness at 3 months, 6 months or 9 months, anymore than there is to do the same for mono, or a staph infection, or anything else. Same with a broken bone or a stroke causing injury.
It's the same illness. The fear of labeling is misguided by the old belief system about how it makes it 'real' and chronic. People need to know what is happening to them, so do doctors, and if it means that in reality, recovery rates for ME after 3 months, are 50%, then that's what it means. People still need the opportunity for time off work, to get support and help the natural recovery process, preferably with professional support based on scientific evidence. Instead what we have is decades of recorded lies, invalid data and even worse conclusions.
All of this is driven by the denial and awful research that lead to the notion that recovery is rare, simply because the real denominator was never counted properly. It's true that it's rare, but only after a certain point. It is still the same illness. I'm sorry but medicine is supposed to be scientific, they need to grow the hell up here and fast. Labeling things does not magically change the outcomes per se, but they certainly can improve outcomes by actually recording what is happening and working with reality, instead of some odd mix of fiction and distorted facts.