What is the best way to do a security cleaning on my Mac Desktop

Stop unwanted Notifications - Apple Community describes how to fix unwanted Safari Notifications. Google must have an equivalent setting. Try their help pages.

Do not download or install any "cleaning" or "security" products. All those things are scams. Unfortunately scams are all you will find if you were to Google in search of a fix.

Notifications are not malware. They are the result of deliberately agreeing to have them appear. Their appearance is intended to deceive you into installing something that really is malware. Don't do that.

You can check your extensions in your chrome settings. There are most of the times some unwanted extensions that give this annoying popups. Your mac is most likely not infected.