What is the technical term for bleach?

Answer 1

"Bleaching agent", perhaps? If you're asking what plain old regular 1960s style Clorox and similar products are, it's a roughly 5% solution of sodium hypochlorite in water. "Color-safe" and "lemon fresh" and every other permutation is something else, so it's hard to answer your question definitively.
(The bleach that's used for hair is usually a peroxide of some kind.)

Answer 2

The scientific name is Sodium Hypochlorite.

The chemical formula for pure bleach is NaOCI and for household bleach it is NaClO.