I think my last name is Hovhannisyan but my mom says it’s Parkhomchuk how do I find out my real last name ?

I think she would know best.

You get your birth certificate out and read what it says, that is your legal name

Legally, it's whatever is written on your birth certificate.

In everyday use, it's whatever your parents say it is. Whatever YOU think it is comes a distant last, although that's not to say you're wrong as what you believe may be the same as your birth certificate.