This is probably more suitable for the philosophy StackExchange.
You would need to choose a definition of "person" to answer this. If by "person" you mean "the physical body of a H. sapiens," then yes, that would be two persons with a common consciousness. However, "personhood" is often attributed to a single conciousness, so that definition would suggest a more accurate wording is "one person, one consciousness, two physical H. sapiens bodies."
As an imperfect example, consider the movie stereotype of identical twins. Twins are obviously not a "common consciousness," but they share enough similarity that movie characters often start treating them as one entity. At the extreme, such as in sci-fi where aliens warp the minds of twins so that they always talk in unison, the rest of the cast quickly does treat them as one entity.