No one really owns a style
Even though it is irritating when someone steals your exact style whether it be hairstyles, makeup, tattoos, clothing styles, or personalities, or all of the above, just take it a compliment and move on.
The person is obviously inspired by your look and maybe a bit infatuated with it, and they are a less stylish version of you, or possibly a better version of you.
Don’t let it get to. Imitation is apparently the highest compliment you can pay someone, and no one really owns a style anyway. I know it may be your signature look, but pay your imposter no attention. They just like the way you look obviously and don’t maybe have a clue what to do with themselves or know how to put themselves together.
They see you getting loads of compliments and realize you are looking pretty good all the while, so they are trying their best to imitate what they see. Happens all the time if you have something worth copying.
Don’t let it get to you. That is just small potatoes.