In the given question, two statements followed by two conclusions. Take the given statements to be true even if they seem to be at variance from the commonly known facts and then decide which of the given conclusions logically follow from the given statements.

Statements:
Some names are languages.
No languages is a poems.

Conclusions:
I. No poem is a name.
II. All languages are names is a possibility.

Only Conclusion II follows.

The correct answer is Option (2) → Only Conclusion II follows. 

1. Some names are languages. → This is a particular affirmative (Some A are B). So, there's at least some overlap between "names" and "languages."

2. No language is a poem. → This is a universal negative (No B is C). So, "languages" and "poems" do not overlap at all.

Conclusions:

Conclusion I: No poem is a name. This is a universal negative (No C is A). But from the statements:

• We only know that no language is a poem.

• Some names are languages, but we don’t know the relationship between names and poems directly.

It’s possible that some names that are not languages could be poems.

So, Conclusion I does not logically follow.

Conclusion II: All languages are names is a possibility. From the statement "Some names are languages", we know there is some overlap.

This means it's possible that all languages are names — it doesn’t contradict any statement. So, Conclusion II logically follows as a possibility.