From below video it is understood that the jailbreak of iOS 9.3.4 is achieved by Min (Spark) Zheng an Android/iOS senior security engineer at Alibaba. He has recently posted a video to YouTube showing an iPhone 6 allegedly being jailbroken by an app dubbed OverSky (aka Flying). The iPhone is running iOS 9.3.4 as it can be seen in the video.
If they decide to release the new jailbreak for iOS 9.3.4 it will be called OverSky jailbreak tool.
Previously we came to know that Appale has already blocked the access for jailbreaking iOS 9.3.4 by patching it and now also the latest revision i.e. 9.3.5 is also released.