UCC Section 4-403 (you need to check your state's version to be sure it reads the same):
(a) A customer or any person authorized to draw on the account if there is more than one person may stop payment of any item drawn on the customer's account or close the account by an order to the bank describing the item or account with reasonable certainty received at a time and in a manner that affords the bank a reasonable opportunity to act on it before any action by the bank with respect to the item described in Section 4-303. If the signature of more than one person is required to draw on an account, any of these persons may stop payment or close the account.
You have to read that in conjunction with section 4-103:
(a) The effect of the provisions of this Article may be varied by agreement , but the parties to the agreement cannot disclaim a bank's responsibility for its lack of good faith or failure to exercise ordinary care or limit the measure of damages for the lack or failure. However, the parties may determine by agreement the standards by which the bank's responsibility is to be measured if those standards are not manifestly unreasonable.
Read together, this means that the UCC says the customer has to describe the check with "reasonable certainty" but doesn't define what that means. However, your account agreement should further refine that by specifying that the customer must provide certain items in order for the stop to be effective (usually this would be at least amount and serial number of the check because that's what the bank's software uses to kick the item out, and the payee).
Nobody's perfect, not even a perfect stranger.