They actually go by many names. Most businesses will refer to them as a dishonored check, meaning that you wrote a check that your bank then refused to honor. Other common terms include bounced check, squishy check, and a rubber check. Banks often refer to them as non-sufficient funds check, because your account did not have the required funds.
Business will often receive a bad check, one that the account it is from doesn't have sufficient funds to cover. These checks are often called rubber checks, because they bounce back to the business.
Alternative names for a "bad check" are "inadequate funds," or, more commonly, a "cold check. " There are few legal terms used beyond these, except "lack of payment" or "fraud" in severe cases.