Revealing true family names would do no good for anyone involved. Estella has been raised thinking that she has known nothing but wealth and prosperity her whole life. To find out would link her to Magwitch, a convicted felon, and Molly, a woman who should have been convicted for murder. That would only bring embarrassment to Estella.
As for telling either of the parents involved, they would want to contact Estella. They would be proud of her and want her in their lives. She, however, would want nothing to do with them. It would only bring misery to all of them. So Pip keeps his mouth shut. The only person he reveals it to was Magwitch before he dies. All he said was that he knew his daughter and he loved her.