‘Oakbournes’ is an invented word, as far as I can tell, made from concatenating ‘oak and ‘bourne’.
Oak
The oak is seen as a tree of great strength – with ‘Hearts of Oak’, which is literally the middle of the oak tree, symbolizing the bravery. The oak is seen as the national tree of England [1], and famously Charles II is supposed to have hidden in an oak tree at Boscobel, near Wolverhampton.
Bourne
The Oakbournes is on the Bishopdown Farm estate, and therefore in the Bourne valley – Bourne derives from the Saxon word for river – ‘burna’.