I think I know what your getting at but I also think because of the fluency between positions you couldn't call anyone prop as very often they won't be proping scrums.
I'll have a go though.
1/fullback - second playmaker
2/winger - winger
3/centre - attacking centre
4/centre - defensive centre
5/winger - winger
6/stand off - playmaker
7/scrum half - organiser
8/prop - driver
9/hooker - distributor
10/prop - driver
11/second row - wide runner left
12/second row - wide runner right
13/loose forward - optional driver.
I don't think there's anything wrong with the fullback name, as that's just where they are.
Winger is also fairly self-explanatory.
I'm not sure about why you have an attacking and a defending centre when surely they should both be doing the same job? I'd just call them a wide/edge receiver or something to that effect.
Back rowers would be wide forwards, and front rowers go forwards.
Hookers a quarterback, because that's where they stand from the ruck.
Halves could still be half backs. They stand halfway back between the ruck and the rest of the players when they make a play most of the time. Usually have one organising (chief) half and one running half.
Loose forward can be whatever the coach decides to use him for! Just a utility forward I guess if there isn't a specific role for him.
So there you go. When they abolish the scrum, here's some names!