According to a redditor named H3x0n that received a pairing notification for his smartwatch, he noticed a new logo along with the Wear OS designation. 9to5Google adds that the notification was sent via Google Play Services, which is currently at version 12.2 (most recent stable release). However, H3x0n is running the newly released Android P Developer Preview, which is running version 12.4 of Google Play Services.
With the 12.5 beta, both the new name and the new logo are present. The logo now shows a stylized "W" comprised of Google's corporate colors, two slashes, and two dots.
While signs of the Wear OS rebrand have shown up courtesy of Google Play Service, we cannot say the same for the Android Wear app (although there more certainly will likely be changes as we approach the final release of Android P).
What remains to be seen is if there will be a new flood of devices announced alongside Wear OS. There hasn't been much activity on the [device side of the] Android Wear front in recent months, and Apple is said to be pretty much dominating the wearables segment. We'd like to see more Android OEMs step up to challenge the likes of the Apple Watch, but many consumers still don't see the need of adding another smart device to their repertoire. So we can understand why some OEMs are apprehensive at the moment.
Google appears to be in a rebranding mood these days, as it recently combined Android Pay and Google Wallet into a single brand: Google Pay. Google Pay will be used across all of Google's platforms and services including Android, Chrome, YouTube and even for NFC-backed purchased in retail stores.