Sometimes yes, but not always, and it depends on the supplier the booking came from. Some hotel suppliers accept a change request on a live booking through the API, so your staff can ask for different dates on the same room. Others offer no change option at all, and the only way to move a customer is to cancel the booking you have and make a fresh one for the new dates.
What really decides it is the rate your customer booked. A refundable rate that is still inside its free cancellation period can usually be cancelled and rebooked without a penalty, although the new dates will be priced at whatever the hotel is charging for them now, so the amount can go up or down. A non refundable rate is a harder situation, because cancelling it normally means the money is lost and the hotel is under no obligation to move the stay for you.
Your portal shows the cancellation terms that were saved with the booking, so your staff can read the room's actual policy and its deadline before promising the customer anything. Where the supplier does support an amendment, the request is sent and then waits for the supplier to accept it, so treat it as requested rather than confirmed until the reply comes back. A small correction to a guest name is often easier to get through than a change of dates, but that too is the supplier's rule and not something we can override.
Open the booking in your portal, look at the cancellation deadline on the room, and then decide whether cancelling and rebooking is the cleaner option for your customer, or whether it is worth asking the hotel for a change first.