If an object moves at constant speed, does it necessarily have constant velocity?
No, it doesn't. Velocity is a vectorial quantity, it has magnitude (speed) and direction. Uniform circular motion can be given as an example in order to help you with your question. Even though the speed is constant in this particular example, the direction changes all the time.
The velocity of an object changes when the net force acting on it is not zero. When the net force is perpendicular to the velocity, it does no work and the kinetic energy of the object remains constant, so the force only changes the direction of velocity not the magnitude (speed).
If an object moving at a constant speed, It is not necessarily that it should move with constant linear velocity because Linear velocity is speed along with direction. so if the direction is not constant then Linear velocity will vary.
e.g - An object moving with constant speed in a circular path certainly doesn't have constant linear velocity because its direction keeps on changing at every instant tangentially. However, Its angular velocity will be constant.
Please note that the only condition the speed and the linear velocity be constant if the object travels in a straight line path without u-turn