I'm faceblind so pretty much everyone looks like everyone else to me anyway.
So if somebody had similar hair to me I'd probably think they looked just like me, even if they looked nothing like me.
But I've never really thought too much about what I'd do with people who looked like me. I never really bothered to memorize what I look like (or really what my hair and eyes look like) the way I do with other people because it's not like I'd have trouble finding myself in a crowd.
So if I saw somebody who looked like me, I'd probably barely register it since I barely know what I look like in the first place.
But if they hung around me enough I'd get so sick of everyone else saying "Wow SoAndSo looks just like you!"
Although one time when I was walking home from school, I saw a man in a car who I thought looked exactly like my best friend. He had similar clothes, the same hair, he even smiled at me in the exact same way!
I later asked him if he had been in the city (he lives in another state) that day and he said no, so I knew that the mystery man couldn't have been him. Whether he actually was my friend's doppelgänger or not remains a mystery.