I keep getting Virus alerts from update-mac.com. Is it valid?

No. The backers of that site are trying to scare you into buying useless anti-virus protection.

No one—not even the Mages and Wizards in Cupertino—can "see" what is on your computer without your giving express permission for them to remotely access your device. All "virus detected" messages are scams.

These notifications are probably coming from Safari.

Open Safari and, in the menu bar, click Safari > Preferences (or Settings, depending on your version of macOS), click the Websites tab and select Notifications in the sidebar. In the list of websites to the right, remove the websites you do not recognize. Note that in the example below, I have no websites at all in my Notifications:

Great! You are most welcome!