Have class with this sexy girl
Sit next to her
Read body language and can tell she wants me to notice her
Next day pick difference seat to see what she does
She sits next to me, knowing another girl sits there that I talk to.
Decide to go for it
Make small convo and later on mention"your name is Jessica right?"
Replies yes, your name is James right?

I wanted to reply B**CH.... WHO THE **** IS JAMES?! But I carried on like it didn't bother me.

4th day of class, teacher calls out names for attendance I was hoping she would know it since I sit next to her....... Kind of turned off by this, actually turned off a lot by this. Did she just make a simple careless mistake or did she not give a damn what my name was from the beginning.

It can mean 2 things:
1. To her, you are absolutely nobody. She never noticed your name and she is not interested;
2. She is testing you. Of course she knows your name, but she doesn't want to show too much interest and therefore pretends not to know your name.

If you replied with "B**CH.... WHO THE **** IS JAMES?" then you failed the test and she will think you are an agressive, frustrated guy (it is just a name , why this reaction?).

Actually, she knows that you know that she knows your real name. She was hoping that you use this to have a flirty chat. If you could use this moment, you could game her.

- "James? Who's James? Last night in bed, you were screaming James too. WHo's james???"
-'OMG, are that shallow? That you think all guys are James"?
- 'Yes, I am james! How did you know? (and let her talk her way out, and of course you neg her)
-"aha! You are like that huh? (=neg) We have been intimate for such a long time and i shared all my secrets with you, and you still don't know my name??!!"

Of course, you are free to use any line you want. I hope you notice that every one of the lines above are more helpful than your line (B**CH.... WHO THE **** IS JAMES?!)