macOS Catalina has updated Gatekeeper in a way that makes it harder than ever to install software that doesn't come directly from Apple's official channels. Now, even if you have set your Mac to "Allow Downloads from Anywhere" you will still receive the following error message when you try to run the ZBrush installer:
"ZBrush_2020_Installer" can't be opened because Apple cannot check it for malicious software. This software needs to be updated. Contact the developer for more information.
When you get this message, go to your Mac Settings >> Security & Privacy >> General tab. There you will see the ZBrush installer listed, along with a button to "Open Anyway." This will launch the installer despite the fact that it didn't come through the Apple store.
Please see this Apple support article for detailed information.