I'm annoyed that my sister in law introduced me by my brother's name to her daughter
This sounds like an honest mistake. Why are you annoyed over this?
I think that is real awkward. I don't like at all to be compared to my brother.
It is understandable that you do not want to be compared to your brother and want to be introduced by your name and not your brother's name. But you should forgive people's mistakes. It was an honest mistake.
I have to correct her every time she introduces me. I hate it.
She might be doing this unintentionally and doesn't realize what she is saying subconsciously. Let her know what she is calling you and remind her what your name is just in case. A little correction can clear up this little confusion.