The Septuagint has a different take on the "queen".
Nehemiah 2:6 And the king, and his concubine that sat next to him, said to me, For how long will thy journey be, and when wilt thou return? and [the proposal] was pleasing before the king, and he sent me away, and I appointed him a time.
For a bit more on the word "queen" in the Masoretic text (KJV), Strong's says this as regards the Masoretic text. "שֵׁגָל shêgâl, shay-gawl'; from H7693; a queen (from cohabitation):—queen.
The context of the meeting was Nehemiah had brought wine to the king when he was sitting there.
Nehemiah 2:1 And it came to pass in the month Nisan of the twentieth year of king Arthasastha, that the wine was before me: and I took the wine, and gave [it] to the king: and there was not another before him.
Nehemiah was sad. It was not kosher to appear before the king like that, but Nehemiah asked for permission to rebuild. The king agreed.
So, why was the "queen" or "concubine" sitting beside the king? Jamieson suggests it may have been Esther. She had success in turning back evil and in helping preserve the Israelites. We find this hint also.
Esther 7:2 And the king said again unto Esther on the second day at the banquet of wine, What is thy petition, queen Esther? and it shall be granted thee: and what is thy request? and it shall be performed, even to the half of the kingdom.
The name of that king was Ahasuerus with Esther, but some believe it the same as Artaxerxes with Nehemiah.
So, the king and queen were fully married as husband and wife. They helped the Jews rebuild their temple. She was mentioned as present most likely because she was well-known.