You can keep calling her Sophy, Sharon. Why not? It's your rose. Sue's going to call her new rose Geese Lane because it's easier to remember and pronounce than Ghislaine de Feligonde, and I usually call Baronne Prevost "You Miserable Wretch" because it has no resistance whatsoever to pests or diseases.
I'll wait a day or two before moving your photos in case someone else in the forum thinks that's the wrong identification and has another idea.
The perfect foliage on the rose bush and the amount of reblooming really sound more like a Buck rose than an Austin. You have the perfect climate for Buck roses.
