I echo all the above. And would even challenge you – why fear the label? There really isn’t stigma, and I suspect you are already on the way to appreciating that it really is a learning difference, not disability.
In addition to testing and accommodation (and maybe meds) I strongly urge you to get executive functioning tutoring. My ADHD son had tutoring 3x a week in 9th grade, 2x a week in 10th, 1x in 11th and then none his senior year. You want your son to learn techniques for dealing with his ADHD in college and beyond, where there are fewer or no accomodations. Set him up to function without the supports – eventually!
My son had a low gpa that improved over time, and scored very high on the ACT. He wrote about his ADHD in his essay (in the context of his hard manual labor summer job). Because of his profile we applied to 4 reach schools, 2 match and 4 safeties. He got in everywhere but 2 reaches. I would not have believed this possible when he was in 9th grade.
Also, the testing will help you understand his difficulties. Otherwise it is all to easy to say “What do you MEAN you forgot to rewrite the paper???!!! How could you forget?” (are you incredibly lazy being the unspoken subtext). That is super damaging to bright kids who want to do well.
Finally, my son had a lot of physical symptoms related to his anxiety due to not doing well in school – migraines, stomach aches etc. Just something to keep in mind for your son.