Thanks to TP Friend Paul Dianzen for the heads up!
Android 2.3.4 Gingerbread Update, which brings a slew of software enhancements including 3D Sweep Panorama camera, 3D gallery, screen capture, full Facebook integration in multimedia apps, phonebook and calendar, and improved TimeScape UI, is now out for Sony Ericsson Xperia Neo!
To get this update, just connect your Sony Ericsson Xperia Neo to your PC via USB and run Sony Ericsson PC Companion. Wait for the software update notification to pop up, then download and install the files.
You may also check if you can download the update over the air. Go to Settings, About the Phone, Software Updates, Check Now. If you don't get the OTA upgrade notification, do what's written above.