hawk moth is Gabriel Agreste and i have proof in season 1 episode 18 with Simon says he asked ladybug if he could look at her earrings and i think he was trying to take them because he looked so sinister and yes the face structure is not the same but here is another reason why its him in the same episode when ladybug captures the Akuma unlike the other episodes where hawk moth appears with anger he does not appear when the Akuma is captured because hawk moth or Gabriel Agreste is not at his house or evil lair and when Gabriel hugs his son/Adrien he noticed the ring he asked his son/Adrien about the ring and if you still dot believe me here is one more reason in season 1 episode 26 Adrien finds a book about all the miacculous and all the owners and just before gabriel walked out of the room it looked like he was studying the book so thats why i think hawk moth is Gabriel Agreste.