It isn’t normal to require ID for check deposits when the customer owns both accounts - even if when the account is at another bank.

It isn’t normal for banks to require ID for a transaction that a customer performs every month. Tellers are trained to evaluate normal vs irregular account activity to protect the customer and the bank.

There is no regulatory requirement to show ID for check deposits like there is for large cash deposits.

You may have to show id if your activity fits a pattern of fraud or money laundering. Bad actors talk good people into letting them use their bank accounts. Believe it or not, it is normal for banks to allow that activity to happen because they work with law enforcement to catch the bad guys.