Haman had a wife and friends. When a misfortune happened to him, the Megila doesn't speak anymore about his friends but about "chachsmav", which we can perhaps translate as his experts.
Are they the same people? If yes why change their name?
This question is asked by the Gemara Megillah 16a. The gist of it is that since at that point Haman's advisors said words of wisdom, the Megillah calls them 'Wise Men', to teach us that anyone who says words of wisdom, even if they are not Jewish, deserve to be called 'Wise Men'.
ויספר המן לזרש אשתו ולכל אוהביו וגו' קרי להו אוהביו וקרי להו חכמיו אמר רבי יוחנן כל האומר דבר חכמה אפילו באומות העולם נקרא חכם The following verse states: “And Haman recounted to Zeresh his wife and to all his friends everything that had befallen him. Then his wise men and Zeresh his wife said to him: If Mordecai, before whom you have begun to fall, be of the seed of the Jews, then you will not prevail over him, but you shall fall before him” (Esther 6:13). The Gemara comments: At the beginning of the verse it calls them “his friends,” and in the continuation of the verse it calls them “his wise men.” Rabbi Yoḥanan said: Whoever says something wise, even if he is from the nations of the world, is called a wise man.
A slightly more 'Drushy' answer is given by the Sfas Emes in his Likutim (can be found in the Artscroll book Days of Joy: Ideas and insights of the Sfas Emes on Chanukah and Purim):
The Sfas Emes ties this to the Mishnah in Avos 5:16 where it says that a love which is based on something will cease to exist when that specific 'something' ceases to exist as well. Those who loved Haman loved him for his wealth and power, when he started losing his wealth and power, they no longer loved him.
Up until this point in the story, Haman was an exorbitantly wealthy rising political figure. He had power and money, so there were lots of people who became his 'friends' for those reasons. This point in the Megillah is where Haman's fortunes begin to turn, so immediately, all his 'friends' dropped their pretense and were only described as 'advisors'.