We all know that famous means well-known.
The goof comes when we use notorious as a synonym for famous, or notoriety as a synonym for fame.
Infamous and notorious mean famous FOR A BAD REASON. If someone achieves notoriety, it’s for doing something you would probably be ashamed of or embarrassed about. The bombing of Pearl Harbor in 1941 has been called a day “which will live in infamy” (italics mine). That’s an excellent and appropriate use of the word.
So unless you’re a complete contrarian or something of a sociopath, you shouldn’t want to be infamous or notorious. That simply means you’re well-known for doing something wrong or dumb. We also shouldn’t be calling someone notorious just because they’ve become famous for something. That’s incorrect and an insult.
One can be both famous and infamous, of course (e.g., people with the last name of Kardashian). Personally, I don’t want to be famous, but if it happened for something good, then that would be OK. But I would never want to be infamous or notorious.
If you do want to be infamous or notorious, talk to a counselor. Seriously.