Summary: I think notability is the best choice, but I think it is worth exploring why.
In my experience (US English), such words generally have varying connotations that might impact your usage.
The following suggestions from other answers imply the subject is known in a positive context:
- celebrity status
The plain text words have more to do with public appeal, whereas the bolded words imply a finer quality: perhaps holding an important title, having earned a prestigious award, or having established themselves as a giant in their field.
Conversely, these words imply that the subject is known in a negative context:
That leaves these suggestions:
"Well-knownness" and "knownness" feel very informal, like the speaker is intentionally making up a new word.
"Reputation" concerns not merely whether a person is known, but what they are known for. Are they renowned/famous or notorious/infamous? If you just want to know how well-known a person is without the qualitative judgment, this isn't the best choice.
"Awareness" and "recognition" are awkward in this sentence structure.
I want to know the [awareness/recognition] of this actor in other countries.
Here it seems to be talking about what the actor is aware of/recognizes, as opposed to how much others are aware of/recognize the actor. "Recognition" is closer than "awareness", and would probably be understood, but is not the best fit.
"Visibility" technically concerns discoverability. One can be highly visible but not yet well known.
The best fits are "recognisability" and "notability". To my ear, these address strictly how much someone is known, without any positive or negative connotation. "Recognisability" is a bit unwieldy, so I would give preference to "notability".
Notably, this is the word that Wikipedia uses to describe the quality of a topic that is worthy of an article.