N.Y. Comp. Codes R. & Regs. tit. 9, § 4220.15
Provided the identity of the horse is satisfactorily established, incorrect or imperfect description in the entry of a horse or failure to register a partnership may be corrected at any time before the horse is announced as a starter and his number exhibited in the race concerned, or in a handicap before the weights are announced; but this section shall not be construed so as to allow any horse to start in any race for which he is not otherwise completely qualified under this Part.