It depends on the hotel. Most of the time, yes a surcharge applies for any additional staying guest beyond the original capacity of the room -- for instance, having a third guest in a two-person room.
It's not as clear in cases where the room already comes with enough beds to accommodate your guest(s).There may be no fees as many hotels charge per-room, not per-guest (unless breakfast is included). However, some hotels may still charge for any extra staying guest beyond the original number of guests mentioned in the booking. Many hotels require all staying guests to register their details.
Note that not all hotels allow extra overnight guests, so it's best to check beforehand.