Earlier today, Facebook has added a handful of new selections on the Gender drop-down box under the Basic Information page.
In accordance to this new feature, LGBT users can also set who can see their gender and how they are addressed, particularly on Birthday Notification.
To access/change your Gender on Facebook, just click on Edit Profile, then click on Edit on Basic Information. Afterwards, click on the Gender menu, select Custom, and then type the gender that best describes your orientation/preference on the box. In that same dialog box, you can also set who can see your gender and tick an option under “What pronoun do you prefer?” menu.