In due time MoneyGram separated from the Western Union and became an independent brand. If you need to cancel or change a transaction, then you should contact by telephone with the MoneyGram branch agent, made the transaction for you. The company continues to automate and enhance MoneyGram MoneyGram launched a new in-person bill payment service which will be delivered through agents in their domestic network, giving consumers an easy, low-cost method to pay their bills. MoneyGram Until 2004, the owners of MoneyGram were Viad Corp and Travelers Express Company Inc.