What Is the Term for an Option with a Delta Very Close to 1.0 or -1.0?

An option with a Delta very close to 1.0 (for a call) or -1.0 (for a put) is commonly referred to as a "deep in-the-money" (deep ITM) option. These options behave almost identically to the underlying asset, meaning they have a high correlation to the asset's price movement.

They carry very little extrinsic value and primarily consist of intrinsic value.