What does forrester's name symbolize?

Did you mean the husband Captain Daniel Forrester or the wife Mrs. Marian Forrester?

both

I think the symbolism pertains to the Captain. For the captain, there is a rugged sense of adventure about him, hence his name "forester". The novel opens at a time when he has already been physically destroyed by a fall from a horse. After suffering two strokes he eventually dies, signifying the end of the pioneering era. I don't think his wife, small town aristocrat, was ready for the type of man he was.