The answer depends on the laws of your state governing minors. Some states allow minors to enter into a legal agreement such as a deposit contract, if they can sign their name some do not. Most states have some form of the Uniform Transfer to Minors Act where a responsible person is the custodian of the funds on a minor's behalf and the minor wouldn't sign at all.
If you are seeing inconsistencies, it means your new account staff is making it up as they go along which could present financial and legal risks for the bank down the road.
For what is and isn't permissible in your state and to establish specific procedural requirements for your institution, you should ask legal counsel to review state law.
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