I registered to a client with a Bitcoin address on Blockchain.info and after some time that address I registered with was changed. I need to pay a fee to the client. Will it reflect to them that even though the address they are receiving from is different but it is the same wallet?
No, they would not. In Bitcoin, wallet is an abstract concept as it is just a software that manages your private keys and addresses. The addresses generated from the private key in your wallet bear no resemblance to others. Unless you explicitly mention it to them that it is your address, there is no way of knowing whether it is you who has sent the bitcoins to your client. From their perspective it might be as they received a 'donation' of bitcoins from some random person.