Using the message signing feature of Bitcoin-Qt can be a possible solution. It works like this:

1) A customer sends x coins from address AddrC to the merchant's address AddrM;

(Now the customer needs to prove that she did send the fund)

2) The merchant generates a unique token (can be a random string) and asks the customer to sign it with the private key to AddrC;
3) The customer signs the token and the merchant verifies it;

(Now the merchant knows who sent her the fund)

4) The merchant delivers her product or services.