Earlier this week, it was spotted in a Google Play Services beta that Android Wear was to become rebranded as Wear OS. Today, that change is official, as Google has launched a new website for its newly-named smartwatch operating system.
Of course, it's entirely possible that you might miss the new branding on the site, as it's in small letters in the top-left corner. There's also a note at the bottom that 'Wear OS by Google works with phones running Android 4.4+ (excluding Go edition) and iOS 9.3+".
To be clear, nothing else is changing at the moment. It's just a different name for the same product. There should be an update for your device, as well as for your Android Wear app on iOS or Android. The app update is live already for Android (now called Wear OS by Google Smartwatch), and it will presumably arrive for iOS over the next couple of days, due to Apple's longer approval process.
Presumably, the change is to make the platform more friendly for iOS users. Android Wear certainly sounds like something that only works with Android, and it could be especially so for an iOS user that's used to Apple products only working with iOS devices, such as the Apple Watch.
But Wear OS is a different story. These smartwatches are mostly standalone products now, with the devices connecting to Wi-Fi and sometimes cellular networks, and their own Google Play Store to download apps. If any functionality on the platform is limited on iOS, it's minimal.