Oh, which are the biggest names is debatable. They are all well-regarded schools. On these boards, the parents most interested in prestige talk a lot about Choate, Deerfield and Hotchkiss, among those you mentioned.
The main point is this: your kid is too young to be in 10th grade at boarding school next year. He’d be exposed to too much before he’s emotionally ready, and, depending on what sports he plays, he’d be in physical danger on the athletic field. For example, a 14-year-old going up against kids as much as five years older in various team sports would be at high risk of physical harm from collisions with much bigger and stronger students.