As pointed out by MacRumors, beta versions of Mojave started to alert users that Back to My Mac will end soon. An Apple support document (posted on August 9, 2018) confirms that the feature will not be supported in Mojave.
What is Back to My Mac? It allows users to remotely access Macs to perform file sharing and screen sharing. It requires the Macs involved to use the same iCloud account and run at least OS X 10.7.5 Lion.
If you don’t upgrade to Mojave, you can still use Back to My Mac. Apple has a support document on how to set it up.
Alternatives to Back to My Mac
If you do plan to run Mojave but rely on Back to My Mac, here are some workarounds for when the feature disappears. Apple also has a support document to help you prepare.
If you want files to be available on multiple Macs at all times, Apple recommends using iCloud Drive and the Desktop and Documents Folders option. Here’s how to turn on Desktop and Documents, as well as some tips on getting the most out of Desktop and Documents.
If you simply want to transfer a file from one Mac to another on the same network, you can use AirDrop
MacOS has a screen sharing feature built in. You can find it under System Preferences > Sharing. In the box to the left, mark the checkbox for Screen Sharing. You can specify what users can perform screen sharing, or all access for all users. Here are the details for setting up screen sharing.
Use Apple Remote Desktop to manage remote Macs
Apple recommends the Apple Remote Desktop app ($79.99) for more in-depth remote-Mac management.