Q. I completely agree with Krishna’s being the source of all identities of God, including Lord Vishnu (Bg. 10.8). However, I have a different explanation for the identity of Lord Narayana. Etymologically, Narayana consists of two parts: nara, “living beings,” and ayana, “ultimate goal.” Thus, Narayana means the ultimate goal for all living beings, namely Krishna. (Everything else we do is Prayana, “a sojourn.”) Therefore, the name Narayana is congruent with Krishna Himself.

Ans : Thank you for the analysis. We might add that all names that indicate the Supreme, including the name Narayana, naturally refer to Krishna.
But Lord Krishna is generally not referred to as Narayana, except when He manifests a four-armed form. And that form is considered to be  in a sense, lower than the two-handed form of Krishna. For example, Krishna once hid from the gopis by taking on His four-handed Narayana form.

The gopis respectfully offered obeisances to “Narayana” but kept looking for Krishna, who alone can please them.