In Megillat Esther, the Pasuk (2:3) says that Achashverosh gathered the girls and placed them in the women's house, and the one who guarded them was הגא (ending with an א and with a segol under the ג). In Pasuk 8, his name suddenly changes to הגי (ending with a י and with a kamatz under the ג). I assumed this was just a matter of grammar, since the second name has an אתנח under the word, which would normally change a segol to a kamatz. But I'm a little skeptical of that answer, since the last letter was also changed to a י. Is that also just a matter of grammar? If anyone has another explanation (sourced, please) to the change of name or can verify my own answer with sources, please do so.
Rabbi Levi Yitzchok Shneerson explains this discrepancy Kabbalistically (Likkutey Levi Yitzchok (Pesukey Tanach Umamareh Chazal pg. 95, see Sefer Ha'erchin Chabad (Mareches Ha'osyos vol. 1 pg. 369)). The main idea is as follows: There is a concept in Kabbalah known as the "18 Women of Leah" (which is why a king may marry a maximum of 18 wives). This is comprised of "9 Women of Gadlus" (big), and "9 Women of Katnus" (small). Since he was the "Keeper of the Woman", he was named הגי which has the numerical value of 18. However, at first he had only attained the level of the "Nine Women of Katnus", and was then known as הגא which is only equal to 9.
The Rokeach (2:8) writes that he was first known as הגא which in א"ת ב"ש becomes צר"ת (“rival of”) since each women was a rival to the next. However once Esther came, he became הגי, which in א"ת ב"ש is צר"ם – (their rival) - because she was the challenger to all the others.
In the commentary written by R' Nessanel ben Yeshaya to Megilas Ester (on Esther 2:3, printed in Sefer Zikaron Leharav Yitzchok Nissim vol. 3 pg. 349) he explains that he was originally called הגא because he would not talk allot. After he became "The Keeper of the Woman", he became influenced by the "שיחת נשים" (abundant women chatter) and was thereafter known as הגי.
The Sefer Ir Mivtzar writes in the name of the Alshich that the miracle of Purim happened through the Divine Name of Yud-Kay. Based on this he explains that חרבונא was later changed to חרבונה, and הגא to הגי to symbolize the Yud and Hay.