We've already got "Prime Universe" for the original 1964-2005 continuity, and "prime" means "first." So we could have the Prime Universe and the Second Universe.
I have to say, the mathematician in me shudder at the original continuity being called the "prime" universe, as in mathematics the prime symbol is used for the derivative
of a function. So it should be Trek and Trek' in my book.
I'm weird. I know.