Consider the following:
> as a kanji has the meaning "accomplish", "(to) reach"
>
> as a kanji has the meaning "name" or "reputation"
Kanji compounds:
> : "achievement"
>
> : "famous, celebrated"
>
> : "fame, prestige"
And in Chinese, `(míng rén)` has no connotations of skill as far as I know, it simply means "famous person". `(dá rén)` however means "expert" and does not imply fame.
I would say your assessment is a reasonable one.