Su Qingyue seemed to be lost in her memories, "The Chen Family did have a little girl they had just bought named Su Qingyue, but she was sold off by the Chen Family to who knows where. As for my real name at the time, I was too young to remember clearly. I only remember that the family head of the Chen Family disliked my name, found Su Qingyue passable, and thus, simply decided to call me 'Su Qingyue'."
She had no memories of the original owner of the name. If she admitted to being the daughter of those two money-grubbing old folks, they'd definitely cling to her non-stop, refusing to give up.
So, she simply chose not to admit it, making up a story instead.
Unexpectedly, it later turned out to be a self-fulfilling prophecy—she really wasn't the daughter of the Su Dashui family.
Of course, that all happened later.