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Nicely done in terms of facial angle and lighting for a "broad" lit portrait, but on a dark background broad lighting makes the side of the head and ear, not the front of the face, the dominant tonally defined focal point. To your credit you have balanced the lighting on the face well to prevent the ear from stealing the show as it often does in broad lit shot, but the ear still winds up a bit brighter than either eye or the mouth by virtue of the ear being closest to the key light and the eyes and mouth being further away and shaded by degrees.
Lighting in the style of "Rembrandt" pattern is quite popular but better suited, I think, to photographs like those of pensive or sullen old men to symbolize their descending glidepath towards the darkness of the grave. Here both the lighting pattern, dark clothing and overall dark mood of the photo seem to me out of context with the age of the boy and his expression.
With kids you can make them seem childish or mature with the choice of lighting strategies and overall tonality of the image. So if you wanted to create a "boy becomes man" style confirmation portrait when he is a bit older and wearing a suit (symbolizing the uniform he'll wear and an adult) this style of lighting would be more in context. But for his age and expression and the casual nature of the capture I think short lighting which would put that beaming smile more into the spotlight would have been a better choice. Something more along these lines, which is how it would have looked with him facing into the light.
Again its not a matter of broad lighting being "bad", just that it's not the best match to the overall context and "happy boy" message the photo projects and the dark background. On white backgrounds low ratio broad lighting is actually a better choice than "short" lighting because the tonal dynamic is reversed and the overall attraction gradient is light > dark. But on a med > dark background short lighting, by virtue of highlighting the entire front of the face evenly with strongest light around the cheeks below the eyes and the mouth, will act like a magnet to pull the viewer to the front of the face — and hold attention there. Is after the exact same pose and expression, all that is changed in my edit is the tonal gradient to control where the eye of the viewer is tempted to go and dwell.