Does the rudder need to be held throughout a coordinated turn?
When you deflect the ailerons, you increase lift on one side of the wing and decrease it on the other. This causes a parallel increase of the local induced drag where lift is increased and vice versa. The consequence of that is a yawing moment which needs to be corrected with rudder deflection.

Once your ailerons are neutral, this yawing moment goes away, but now your airplane is in a constant yawing motion which increases airspeed on the outer wing and swings the tail around, so your vertical tail sees some sideslip even if your ball is centered. The airspeed differential between inner and outer wing causes some friction drag differential which tries to pull the aircraft out of the yawing motion. Depending on the tendency of the rudder to follow a sideslip, you will need some pressure to keep the yawing motion going.

It is hard to be more specific, because details depend on the particular airplane.

In most of the airplanes I have flown, you also need to keep some aileron deflection to keep your bank angle constant. Here are two effects which go against each other, so again the details depend on the particular aircraft. One effect is caused by the airspeed difference which causes a lift difference between inner and outer wing. To correct this, you need to deflect the aileron against the bank. The other effect is caused by the different centrifugal forces of the masses of the inner and outer wing. The whole wing is moving at the same angular velocity, but centrifugal acceleration is the product of the square of the angular velocity and the radius of your motion. Since the outer wing flies at a larger radius than the inner wing, the masses of the wing will try to pull the aircraft level. This needs aileron deflection into the bank. If you are lucky, both effects cancel each other out, but normally they don't.