A sex change is hardly the only explanation, but it's a very likely one. Be honest. Let's say my name is John Leslie Roberts and for my entire life up until 2010 I was referred to as John, then I told you to start calling me Leslie from now on. I seriously doubt you would just shrug that off.
If you're wondering how others drew the correct conclusion without additional information, this is how. It's extremely common for those who have had male to female sex change to choose a female root name buried within their current name or names. It's extremely uncommon to do that for any other reason. People associate names, gender and personal identity very closely.
You change one so drastically, there is a good chance you've changed the others too. There is a lot more to that sentence than just a name change.
If it was a marriage that caused the name change, she would have just said that point-blank. No need to dance around it. From the lack of explanation it was pretty clear that it was a sex change.