I think its always been called Acocks Green, even if its not the original site of the Green. That would have been further down the Warwick Rd probably outside Acocks Green House. The home of the Acock family, this was located close to where the Dolphin public house once stood, and now stands a supermarket.
Enough history for today, here are a few more photo's of the present Green from different angles and at different times.
Phil