Yes, I have some confusion here as well. I thought you distinguish by saying sua for her and suo for his. Is that not correct? How else would one differentiate in the following scenario. We are at a meet and greet function. There is a man and a woman out of ear shot and they are talking to each other. We have both met them. I say to you "Non ricordo il suo nome." How do you know whose name I forgot - the man or the woman?
Did you try "his" and it marked you wrong? In this case there is no context specifying "his" or "her" therfor either should be taken as correct. Il suo / la sua matches the noun being possessed (in this case, the name "il nome") and NOT the gender of the person doing the possessing. So you dont say "il suo" for him and "la sua" for her, instead it's "il suo nome" for EITHER his or her name. Or "la sua madre" for either his or her mother. More context needs to be given to specify which in these cases.