First of all, "Chatanim" is the plural of "Chatan," which means bridegroom. This word befits the occasion, for the Jewish People on this day is expressing its love for the Torah and for its Author.
Why is the plural used? How many bridegrooms are needed at a wedding?
In this case, there are at least two. The term merely symbolizes love, and it is possible to love many aspects of the Torah. The two most important chatanim on Simchat Torah are the "Chatan Torah," the Bridegroom of the (End of the) Torah and the "Chatan Bereshit," the bridegroom of the (Beginning of the) Torah.
Who is the "Chatan Torah" and What does he do?
"Chatan Torah" is the title given to the individual who bought the honor at the Auction or the person designated by that buyer (frequently the Rabbi or some other highly respected member of the congregation). He is called to the Torah with a beautiful chant, describing his greatness in glowing (occasionally, slightly exaggerated) terms, and is given the honor of reciting the blessing over the last section of the Torah to be read in the current year, which is the conclusion of Moshe's valedictory address to the Jewish People.
Who is the "Chatan Bereshit" and What does he do?
The "Chatan Bereshit," "Bridegroom of the (Beginning of the) Torah," also a great honor, is called to the Torah with a similar introduction as that which introduced his fellow-chatan. He is given the honor of reciting the blessing over the beginning of the Torah, the section dealing with the Creation of the Universe by G-d, through the Creation of Man, and the Sanctification of the Seventh Day, the Day of Shabbat.