Deal with it the moment you notice, not on the day. A double booking spotted a week out is a phone call; the same one spotted at the door is two annoyed clients and an hour you cannot make up.
Move the one that is easier to move, but tell both. Ring the person you are moving rather than messaging — a call about a mistake lands very differently from a text — say plainly that it was your error, and offer specific alternatives, ideally better ones. Something for the inconvenience is usually worth more than the margin it costs.
Do not simply cancel the second booking and hope. That is how a scheduling error becomes a review.
Then find the cause, because double bookings almost never happen once. The usual suspects are a second calendar you also take bookings in, a booking taken in messages while somebody was booking online, an appointment blocked out in your head but never entered, or durations too short so the overlap builds up during the day.
The permanent fix is one calendar. Everything goes through the booking system — including the client who texts you, whose booking you enter yourself — because the moment there are two sources of truth, the collision is a matter of time.