Can an administrator or an executor of an estate account name an agent signer for the account?

I wouldn't touch that....but it is probably a state issue.

I have always been told that a fiduciary cannot delegate his/her responsibilities. If they can't serve, the court would determine the appropriate person to serve in the fiduciary capacity.

Ditto both of the ladies above.

The answer will be found in your state's law that deals with probate matters. You should check that section of your state law that deals with the powers of an executor. If there is no statute that permits the executor to delegate his/her duties, then you would have to look at the court order appointing the executor to see if there is anything in the court order that gives such authority to the executor. If in doubt, consult with your bank counsel.

I would be surprised if your state law would permit an executor to delegate his/her duties. Permitting an executor to appoint an agent goes against the wishes of the decedent who nominated a specific person to handle the executor's duties (as well as the court's appointment of that person and only that person to serve as executor).