Donation (live and deceased), evaluations, support, housing, testing, financing, blood cells, antibodies, organizations, coordinators, doctors, surgeons, ultrasounds, x-rays, machines, images, scans, meetings, insurance, laparoscopic vs open surgery, risks, benefits, hospital, recovery, donor, recipient....
It's all for the recipient.
But Hashem only put 'need' in the world, so people can have the privilege of giving.
For chessed (kindness) to abound, there needs to be a recipient.
So really it's the donor - who is humbled and tiny and awed - that needs to thank the recipient for the privilege of being involved in saving a life. Incredible.