When you have objects like that, that exhibit properties of direct reflection, you have to be concerned about the 'family of angles'. That basically means that if the surfaces of the object line up to reflect light directly from the light, off the object, to the lens, then you will get those reflections in the photo.
If your object has flat sides, this is much easier to deal with, but when it has rounded surfaces, you probably can't avoid it. In one of my classes, I have the students try to light and shoot a mirrored x-mas tree ball. No matter what you do, if you want any light on the visible side of the ball, the light source will case a reflection on the ball.
But you do have some control. Firstly, the size & shape of the reflection will mimic the shape and relative size of the light source. So if you put a big light, close to the object, you will get a big reflection. If you put a light farther away (and/or use a smaller light) the reflections will be smaller. Many product photographers might choose to use strip lights, rather than round or square lights (modifiers). This can give you a line reflection, which may look better on your object.
Lastly, you can choose to try to 'fill the family of angles'. So that instead of a smaller reflection, the reflection is much bigger, perhaps covering the whole surface of the object. This is something that a light tent might be used for. Sometimes this looks better, sometimes not. Product lighting really has to be taken on a case by case basis.