An updated Apple Support document has revealed the feature Back to My Mac is being discontinued in macOS Mojave (push notifications were also sent to users as well):

Back to My Mac will not be available on macOS Mojave. You can get ready now by learning about alternatives for file access, screen sharing, and remote desktop access.

Back to My Mac was launched with Mac OS X Leopard (10.5) as a MobileMe service, but eventually moved over to iCloud with OS X Lion. The feature, according to Apple, “lets you set up a network of Mac computers that you can access remotely.”

Alternatives to Back to My Mac? Apple says to use iCloud Drive to access files across devices, or use screen sharing to view and control your other Mac. Another way is to use Apple Remote Desktop, which lets users run apps and files on other Macs.

Apple is expected to release macOS Mojave 10.14 this fall, alongside iOS 12, tvOS 12 and watchOS 5.