Here is a quick summary of the reasons why Gabriel Egreste is not Hawkmoth. My first reason is that upon close inspection, their skin tones are different. This could be because of Hawkmoth's location but Gabriel's skin is a lot tanner. Gabriel's hair I doubt is so easily smoothed out to fit underneath that hat as a part of Hawkmoth's disguise. Hawkmoth is also a lot shorter than Gabriel. Adrien's mum seems to have been a past holder of the peacock miraculous and having had three miraculous in one family seems a bit much. And final reason, in the Simon Says episode, Gabriel was controlled by Simon Says. This would effectively mean that Hawkmoth was controlling himself and between him fluttering around like a butterfly and saying that Simon had to get Ladybug and Chat Noir's miraculous, I doubt Hawkmoth would waste his time doing that. I hope this concludes why he is not Hawkmoth.