I'm not familiar with either word, but just looking at the characters, 達人 would seem to indicate 'accomplished' (ie an accomplished pianist). While 名人 seems more like 'renowned'. Is that a valid assessment?
Consider the following:
達 as a kanji has the meaning "accomplish", "(to) reach"
名 as a kanji has the meaning "name" or "reputation"
達成 : "achievement"
名高い : "famous, celebrated"
威名 : "fame, prestige"
And in Chinese,
名人(míng rén) has no connotations of skill as far as I know, it simply means "famous person".
達人(dá rén) however means "expert" and does not imply fame.
I would say your assessment is a reasonable one.
Both 達人 and 名人 are usually associated with skills in Japanese.
達人 means a person who has mastered everything about something by long-time experience.
名人 usually means a person who has excellent skills. Daijisen also lists another meaning “評判の高い人” (person who is spoken well of), but I think that the usage without connotation with high skills is rare. Daijirin does not state the latter meaning.