You have two choices out of the box: AirPlay and Home Sharing. The main difference is where the operational controls are: on the source computer, or on the Apple TV box (Computers app).
Several third party developers offer similar home sharing solutions (VLC, Plex, Infuse, etc.)
What is the version macOS of the Mac? Find out which macOS your Mac is using - Apple Support
- For AirPlay from Mac: Use in-app AirPlay controls
for apps that have that ability (Apple TV app, QuickTime Player, Safari web video, Prime Video app). Else use system wide Screen Mirroring in Mac Control Center. Some content may not allow AirPlay, as set by the content provider. - For Home Sharing from Mac: Set the source computer to share the library of the TV app. Since macOS Catalina 10.15, that is done in System Preferences (System Settings in Ventura)﹥General﹥Sharing﹥Media Sharing
﹥ⓘ﹥☑︎ Home Sharing﹥. Verify that the Apple ID accounts match on both devices.
The setup is of Home Sharing on the Mac has changed, but the usage is the same as with the iTunes application. Apple Home Sharing sees library names, not computer names, nor folder names, nor app names.