Is there a way to remove all the transaction history of an account? Let's say I have sold my account name, but don't want to show all the old transactions of that account.
No, the blockchain is immutable and distributed.
Due to immutability, any change in past blocks would alter the block hash, making the rest of the chain invalid.
Due to being distributed, anyone can download the blockchain, and it would be difficult to erase it from everyone's memory storage.