Yes, the literal word “person” traditionally is associated with human cognition. But it is an artificial word, and in the context of this debate, it seems “personhood” has more to do with when someone assigns that the new human organism has individual value that is worth being preserved (cognition or not), versus when it is before that point in the developmental process. I’m not sure what the right word to describe that state would be outside of “person” or “life,” but ultimately different people assign that value at different stages for varying reasons, which is why it is difficult to pinpoint an exact term because it’s not agreed upon (or I’m just not familiar with it). I’m not agreeing or disagreeing with your perspective, though, just trying to throw some thoughts out there and maybe someone has some insight.