When unsure of a name, I typically use the Wikipedia spelling — which is Márta in this case.
The simplest way to explain it, both “Martha” and “Marta” are correct spellings of her name. “Martha” is how her name is spelled in America, while “Marta” was her original name in Europe. This difference wasn’t a change forced upon Martha, but a change Martha herself openly embraced. …When Did Marta Karolyi Become “Martha?”