This is not a simple question! But my own suggestion is to avoid the Abhidhamma explanations of this particular term, as the usage in later years is quite different from that found in the suttas.
The underlying sense of the word nāma is “name”. But in pre-rational societies, such as that which Buddhism was emerging from, name has a much more potent meaning. We still feel this when we call an evil Lord, “he who must not be named”. Simply using a name is to invoke the essence of that thing. It was felt that names and the things that they represent (i.e. rūpa) are bound together. When you know something’s name, you have power over it. This is the heart of magic.
The pre-Buddhist Upanishads critiqued this idea, moving beyond the notion of separate rūpas each with their own nāma. Instead, they postulated that, just as when the rivers flow into the ocean, each of them loses their “name” and “shape” and become one with the ocean; so too, each of us will lose our individual “name” (i.e. concept of self) and “shape” (i.e. this corporeal body into which we happen to be incarnated) and become one with the infinite ocean of consciousness (vijñāna).
The Buddha went a step further, showing that consciousness itself depends on nāmarūpa; in other words, our awareness evolves together with the external sense stimuli and the concepts and designations associated with that.
Thus the notion of nāmarūpa is evolving and shifting through this philosophical evolution. It is losing its connection with magic and pre-rational thought, and becoming a rational, psychological idea. This shift is present within the EBTs, which enable us to trace the connections backwards through the Upanishads to magic, and forwards to the hyper-rational explanations of the Abhidhamma, where the connection with magical thinking is lost entirely.