What malware is this and were does it get stored?

Imagine this case: Someone downloads some random apk and, suddenly, it gets downloaded with like a no-named and without icon app. This app sends weird notifications that can't be removed from the phone panel (I guess it is like a bait to click on it) and keeps doing that. When the person goes to setting so as to remove the notification permission, "notifications" suddenly disappears. I guess it also puts pop ups when searching in Google. What is it? Is it stored like deep in the phone? Would doing factory restoration remove it?