This is primarily due to the Westernization of the older game of chaturanga/shatranj, which instead called the analogous piece firz or Firzan, which translates to counselor, or wise man. The pieces are essentially bound by the same rules as modern chess, the biggest difference being that the counselor could only move one square in any direction diagonally (as opposed to the modern queen which can move any number of squares in any direction). There are other differences, such as pawns only being able to move one square, but a pawn reaching the end would also promote it to a counselor.
So at what point did the gender and title of this piece change to the queen? H. J. R. Murray's massive 900+ page tome, A History of Chess, which is still considered the seminal survey of chess history, discusses this (pp. 423-4):
The name 'Queen' is a characteristically European innovation, suggested probably by the position of the piece upon the board and by the general symmetry of the arrangement of the pieces, which pointed to the pairing of the two central pieces. The name has reacted curiously upon the borrowed name fers, and has everywhere altered the gender. All the European names, and even the Spanish alfferza in the Alfonso MS. of 1283, are feminine nouns. We have already seen that the same is true of the Russian word fers.
Originally, the Arabic name was adopted in Spain, France, and England, but was replaced by "Queen" in Italy, Germanic lands, and Scandinavia. The adoption of the Arabic name, as opposed to a translation, suggested that the Europeans didn't quite understand the meaning of the word. The same manuscript cited in the quote showed that the Spanish player associated alfferza to al faris, which means horseman and comes from faras, meaning horse.
This deviation in adoption actually formed two divergent nomenclatures which resembled different philosophies about the game: King, Fers, Aufin, Knight, Rook, Pawn versus King, Queen, Bishop, Knight, Rook, Pawn. The former was more characteristic of the Spanish adoption, which carried on the Muslim/Indian/Persian tradition that chess is a war game, while the latter was more characteristic of the German adoption, which viewed chess as a representation of the European state. As a result, the war aspect is deemphasized and the Queen's presence becomes more necessary.
What was perhaps the most amusing tidbit (although tangential to the original question) was how people would react to the promotion of a pawn to a queen once it reaches the 8th rank. Murray describes it best (p. 426):
In the Muslim game, the Pawn which reached the 8th line became at once a Firzan, whether the original Firzan was still upon the board or not. There was no incongruity in this, for there was no limit to the number of viziers that could exist at the same time under the 'Abbasid caliphate. The same promotion awaited the Pawn in European chess, but the new European game introduced unforeseen difficulties. Not only had the Pawn to change its sex, ... , but by its becoming a Queen when the original Queen was still upon the board the moral sense of some players was outraged. The boldest attempt was the prohibition of promotion so long as the original Queen was untaken.
So in summary, there wasn't a queen in the original versions of the game, which was played in the spirit of a fight or war. The modern variant that has a queen stemmed from a particular European adoption which started using female names for the piece in Romanic languages as far back as the medieval period, even before its move was changed to be more powerful, and viewed the game as more a representation of the European state, which usually had a queen alongside the king.
I got both those links from this comment
Here’s a quick bit of help from u/White___Velvet
Hi there! This is a fantastic question! It is also one that has been discussed previously by one of our flaired experts, the fanstatically named /u/JediLibrarian , both here and here. This is of course not meant to discourage further discussion, but in any event you should find both these threads instructive. Cheers!
https://reddit.com/r/AskHistorians/comments/ap9clf/the_queen_in_chess_is_notable_for_being_the_most/
Edit: Formatting!
Hi, WalrusNjnja!
You may be interested in these answers by /u/JediLibrarian: