[dictum]

To anyone who is interested in implementing this in a product: don't.

To be fair: do it if you must. But don't let the user see the gender field as it changes. If someone has a name that's associated with the opposite gender (or they believe themselves to be of another gender), seeing the change to that gender in the gender field will make them sad, annoyed, or irritated. At best, they will chuckle at the failed attempt to predict their gender.

This is one of those things that, when they work as intended, users don't notice it and it doesn't improve their experience that much, but when it fails, they notice and the annoyance hurts your image.