Many of your symptoms are similar to issues i have had and i am also a number nerd. Forgetting names is a lifelong habit, often being late, and similar school issues, but ADHD is much more than that. As Dr Dodson likes to say, the universal symptoms are an interest based attention system and Rejection Sensitive Dysphoria (RSD). The many other symptoms are what the tests and analysis determine to earn the label.
As to RSD i was amazed when at an ADHD support group meeting one of our attendees woefully admitted to losing patience with a fellow worker that week and loudly berated her for several minutes (it seemed). When our group leader asked “How many of us had a similar experience in the last 6 months” all 12 of us nodded affirmatively. It was an eye opener of the curse that accompanies this condition. RSD