Yes. The obligation to report the claim to the insurance company is dictated by the terms of the insurance policy. If the insured does not timely tender the claim to its insurance carrier, it seriously prejudices the carrier's right to investigate and to preserve evidence. As such, the insurance carrier can deny coverage based upon the insured's contractual obligation to timely report potential claims, especially if the insured is deliberately not reporting the claim.
It appears you are on the plaintiff side in some pending litigation. If the lawsuit is in state court, make sure you or your attorney propound a set of Form Interrogatories (check the box for 4.1 and 4.2) to determine whether there is incurance and the details of such coverage.
Actually, the answer is not a simple "yes" or "no". A defendant is not "required" to provide his insurance company with notice of a lawsuit filed against him or her. However, by failing to notify the insurance company, the insured may lose the benefit of the insurance coverage. If you are the plaintiff and you know who the insurance company is, you can contact the agent or local claims office and notify the insurance company of the lawsuit and provide their insured's name. This may actually force the insurer to retain counsel and defend the action.
As a plaintiff, you can't require a defendant to tender a claim to their insurance carrier if they have one, since they can choose to forego coverage and breach their contract with their carrier and act as though they're self-insured. It seems unlikely that they'd choose to do this if they do have coverage for the claim.
Have you asked form interrogatory 4 to get their insurance information and/or asked them to produce their insurnace declaration page and contact information?
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.