A dyslexia or SpLD assessment is written by one professional who carries out all the tests in person and they then interpret them and diagnose the conditions.
The assessor can only assess for things they have received specific training in and will usually have done extra CPD and, for Maths and Dyslexia, will hold a specific qualification.
An SpLD assessor cannot assess for dyspraxia under the age of 16, but they can often see the educational impact of it and suggest various resources and interventions, they can also refer you on to the right people in your area to do the diagnosis. An SpLD assessor will have a very good knowledge of the various 'pathways' in your local authority.
An SpLD assessor cannot medically diagnose ADHD in a person under 16yrs either, but again they can often spot the behaviours which would suggest further investigation and they will be able to put in a variety of suggestions for educational impact and ways of working with the student to support them.
As there has been some concern about a particular local centre producing substandard reports which make them invalid, I have attached to this a link to a document which can give you some ideas as to what should be in your report. It is not a template for a report and does not look anything like the finished article, but it tells you which sections of a report should be there and which are optional.
Hopefully those of you who are wondering if your report is affected by this will be able to tell by looking at this document.
Here is an example of what a front page might look like and there are highlights on the bits you can look up here; https://sasc.org.uk/Assessors.aspx