Welcome to the forum.
The reflection of the lights in your subject's eyes are called "catch lights'. They are usually something you do want to see, because they give they eyes a sparkle. Eyes without catchlights tend to look dead.
However, you may not want to see too many catchlights, it doesn't look natural. Your example has several catchlights, for example.
Where and if a catchlight appears in the eye, is a simple matter of reflection. The angle of incidence equals the angle of reflection. Basically, the eyes are little round mirrors, and if the angle/position of the lights and the camera match up, you will see them in the eyes. The easy solution is to move the lights so that they don't show up in the eyes.
The usual method is to place the main (key) light so that it produces the lighting pattern that you want. As a starter, position the key light to give you a catchlight at 10 or 2 o'clock. Then position the fill light. A traditional place to put the fill light, is on the camera axis, which is likely to show up as a catch light...but if you place it back farther, the catchlight gets smaller. Many photographers will place the fill light on the opposite side from the key light...at least far enough so that it doesn't show up in the eye...although you could move it higher or lower, depending on your needs, to help hide the catchlight.
Lastly, it's not uncommon to just edit the catchlights. It's pretty easy with digital, but it wasn't out of the question for people to edit them on film negatives, back in the day.