Update [September 07, 2018]: Verizon is now rolling out Agust 2018 security patch for its Moto Z Droid edition smartphone. The OTA update comes as version ODN27.76-12-30-8 and should be available for your device already by now.
Update [June 18, 2018]: Verizon has begun seeding out the Android 8.0 Oreo update for its Motorola Moto Z Droid edition handset. The Android 8.0 build comes as software version OCL27.76-69-4 and should be hitting your device in next few weeks at the max.
Being Android 8.0, you get treated to cool features like picture-in-picture, Autofill, redefined Settings app, notification channels, adaptive icons, smart text selection, revamped notifications center, notification snooze, etc. stuff.
Update [May 26, 2018]: Motorola started rolling out Android 8.0 Oreo to the Moto Z in the U.S. on May 17. The update comes months after it started rolling out in Brazil. It has also been released in India, Europe and Canada, which makes the U.S. the last major market to receive the Moto Z Oreo update.
The update not only installs Oreo but also comes with the latest Android security patch for the month of April 2018. The update installs software version OPL27.76-51 and weighs in at just over 1.4GB, so make sure you have a good Wi-Fi connection.