That's how he will be named Satya instead of Karan.
I think that Satya/Karan will later fall in love with payal's daughter and she will love him as well but when gangu tai will come to know that karan/satya is going to be payal's Jamai then she will relent and refuse the proposal. It might be the moment when she will reveal to Satya that he's actually Karan Siddharth Khurana, Siddharth Khurana's son and that he is actually very rich.
She will tell him that how payal was behind his parents murder and then Karan will obviously want to punish Payal and he will marry her daughter just like Sid married Roshini. Of course when Payal will see Karan, she will not let the marriage happen, reason hes poor and he looks like Sid but like DD, Payal's plans wont work to stop the marriage and then Karan will teach payal the much needed lesson.