I did not experience parental blame but there was a lot of child blame at school and I was accused of making excuses for DS13 because I didn't like the number of detentions and isolations he was in. We unfortunately had to move school. New school was much more supportive.
We had Connors (also completed by school) and an interview with parents and for DS it was cognitive tests, anxiety/mental health evaluation and QB.
The Connors was quite long and asked questions about hyperactivity, defiant behaviour, anxiety etc. the questions were all multiple choice with a rating of never, sometimes, often, always.
I was interviewed mainly about early childhood - milestones, and behaviour age 4-5. (My son is 13). They were also assessing for ASD. My son was assessed in a separate room.
QB was a 20 minute test where he had to press space bar at particular times. It's apparently very boring and you get a graph showing how well you did and this is compared with a reference graph of a child the same age and gender. I don't think QB is always used if Connors and interview is very conclusive.
There were separate tests for ASD which may not be relevant to you, but the screening for that was called AQ (Autism Quotient) and it's available for free online - that is a parent filled out one.
In our area there is a private service which offers assessment via "Right to Choose" but you have to specifically ask for this and there is only one provider they use.
It seems like the processes are all different but your school SENDCO should know and they should be able to put support in place for your son without diagnosis.
My DS went on a reduced timetable and had a timeout card to leave lessons. These were both really helpful and made a big difference for him. It also helped teachers be more understanding and they tried different classroom positioning etc. (This was for six months while we were waiting for assessment).
It can be a long and stressful journey so is helpful if you can find some IRL support, and try and look after your own health/wellbeing. Easier said than done.