In the Megila, Esther is taken from the house of Mordechai - who was clearly known as a Jew, and then Mordechai is constantly expressing interest in Esther ובכל יום ויום מרדכי מתהלך לפני חצר בית הנשים לדעת את שלום אסתר ומה יעשה בה, Esther repeats what Mordechai told her to Achashveirosh in the name of Mordechai ותֹאמר אסתר למלך בשם מרדכי. Why does Achashveirosh not know or at a minimum have strong suspicions that Esther is Jewish?
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Malbim explains (as I think is pshat in pesukim) that Ester was just found in her house, but he was her adopted father, and might have just picked her off the street; she could have been from anywhere. Achashveirosh did have him hang around and give him gifts though, to influence Ester to say who her real parents/origin was when she would see how well Achashveirosh would treat an actual parent or relative of hers.
Achashveirosh did not actually go out and grab each girl from their home and drag them to his palace. He had other people do this for him. See 2:3 ("And let the King appoint officers in all the provinces of his kingdom, and let them gather every beautiful virgin girl to Shushan the capital, to the harem, under the charge of Heigai, chamberlain of the King, custodian of the women, and let their cosmetics be provided."). He also had about 4 years of having different girls paraded in front of him (chapter 1 opens the story "in the 3rd year of his reign", while when Esther is brought before him it's now "the 7th year of his reign"), so he could hardly be expected to remember anything about a particular girl even if he were told about them when they were first taken to the palace.
[Translation taken from Chabad.org]