Double time is rare (common is time and a half). Double time for the SAT takes 2 days, and adds another set of problems for the students and the testing sites.
While ADHD has no formal diagnostic test, typically it is assessed with a combination of questionnaires (parent and teacher) sometimes self report (depending on the age of the client) and associated measures of intellectual, cognitive, memory, alternating and divided attention, organization, executive function, on/off task behavior/distractibility, timed/untimed academic measures, personality/mood screening, etc. Sometimes other things can look like ADHD when the underlying cause may be something else (anxiety, sleep disorders, etc) so the diagnostic testing is a rule out as well as rule in process. With a clearer diagnosis , appropriate recommendations for accommodations can be made
(which might be testing in a quiet room, extra breaks, longer breaks, etc and not necessarily just extra time).
College Board and ACT have specific criteria for evaluations needed for documentatin of the disability. Here is CB’s requirement for documentation of ADHD(a questionnalre will be insufficient) : https://accommodations.collegeboard.org/documentation-guidelines/adhd