No surgeon or hospital who takes their oath seriously would ever perform unnecessary surgery, and I do not mean "cosmetic". I mean a person who is going under the knife for something drastic like that, just to prove a very dubious point.
And such a request would also lead to a psychological assessment, because there are also hypochondriacs and self-mutilators, and they all get screened out.
Not to mention that all transplanted organs have waiting lists and are prioritized according to real need. Every organ wasted is basically one that is denied to someone who really needs it.
This would be like a person asking for a liver transplant just so they can have two and drink twice as hard. The answer would be NO. They could drop money on the table, lot's of it, still NO.
A truly obsessive and wealthy clown would maybe go get surgery in the 3rd world, but it would be from the kind of unethical "doctors" who take organs by force out of kidnapped people.
So basically, either the person is just a nutter and this sketchy clickbait media is taking advantage of it, or the story is 100% bullshit propaganda from the get-go.
No doubt this "outrage" is making the rounds on evangelical forums, working all the rubes into a lather - "Trannies? Abortions? TRANNIES GETTING SURGERY SO THEY CAN GET ABORTIONS ! AHHHHHHHHHHH - Donate now or the end is nigh."