KYC is a one-time activity. Once you complete the rather laborious KYC process, your PAN number is registered in a central database at one of the KRAs (KYC Registration Agency). Opening an account in a different AMC does not require a repeat of the KYC process. You may be required to provide proof of KYC completion, so if you receive a KYC letter from any of the KRAs - NDML, CAMS, Karvy etc., ensure you store it safely.