Quick Scoop: The most likely answer is that the “woman” in question is Natalie Harp , a Trump aide who has been described in reporting as intensely devoted to him and as sparking security concerns because of her behavior around him.

What the reports say

Coverage describes Harp as sending affectionate notes, staying close to Trump, and acting like a highly committed follower rather than a casual staffer. One report even notes Trump dismissed the concern by saying, “She just loves her president”.

Why people call it an obsession

The word “obsession” here is usually used by commentators to describe:

  • Extreme loyalty.
  • Constant proximity to Trump.
  • Personal devotion that goes beyond normal political support.
  • Behavior that others found unusual or alarming.

Another possible angle

If you meant a different woman, social posts and headlines sometimes use “obsession with Trump” loosely to refer to public figures who keep talking about him, including Rosie O’Donnell in one recent item. If you want, I can narrow it down to the exact person you mean.