Will I need ss# for kidney donation?

No. No. However, most kidney transplant program will ask you about your health insurance coverage and support system. You will need to have an annual medical follow-up after donating a kidney. At some programs, not having any health insurance is a relative contra-indication for living donor surgery.
Should not B needed. There should be no questions asked even if ur undocumented resident. All hospital & physicians need to know is that you have 2 healthy kidneys & are fit enough to undergo kidney donation surgery. Good luck.