A non-party can asset the claim only if it is an intended, and not a mere incidental, beneficiary of the contract. Even then, the parties' intent to benefit the third-party must be apparent on the face of the contract. In the absence of clear contractual language of such intent, New York courts have demonstrated a reluctance to interpret circumstances so as to construe such an intent.
CWCapital Invs. LLC v CWCapital Cobalt VR Ltd., NY Slip Op 02240 (1st Dep't April 9, 2020)
Here is the decision.