No, you can't do this.
Even if you could, it would be a nightmare.
What word would you use instead? State, maybe, but while that wouldn't be a huge wrench, it's not quite the right word for the field. I can't think of any word that would be as clear as status or state as to what the field is telling you.
What would you do in places where there is no project context? If you're using status in one project and species in another, which word do you use in a list of reports that include status, or the issue navigator, or the dashboards, or admin, or, most importantly, JQL?
I would go back to your user and ask why they think they want to do this. (I'm now morbidly curious, as I can't think of a sane reason to do this)
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