I thought this is what allowed me to use pins 2,13 for the RX & TX?
It would, except that mySerial is local to setup(). As soon as setup() ends, mySerial ceases to exist. If you make it a global variable, then it would continue to exist, and be usable.
Can I name it anything I want?
Yes, you can.
I was thinking this name was referenced somewhere in the library... No I haven't opened it and looked...
What library? The SoftwareSerial class has no idea what instances of the class are named, nor does it care. Names are not part of the hex file uploaded to the Arduino. They are for people to use.
Ah, a global instance sounds good but I am unsure how to declare it
Move it before setup().
I thought you said;
I did. I was referring to where you use, not declare, the instance. The block I was referring to was from code you posted, where only the opening { was posted.