As it was told by the showrunner that the line arya said to nymeria-'that's not you' was actually connected to the flashbck of the rply she gave to ned stark on having domesticated future.I think the line arya said to nymeria-

'that's not you' symbolizes that arya like nymeria is now no more the girl she used to be in winterfell,as now she is a girl with no name,a path she has chosen of her own just like nymeria.