Patrani Icchini Chauhan
Assuming the question is on the wives of Prithviraja Chauhan, here's the answer.
The Chief Queen of Prithviraj Chauhan was named Icchini Panwar. She was a Parmar Princess and daughter of Salakha Rai as mentioned in Prithviraja Raso. Chronologically she was his second wife but she was appointed Patrani (Chief Queen) and had the highest place among all his Queens. She was the one who presented the problems of Harem and his other queens to Prithviraj Chauhan as their leader. She was also second in command. She is mentioned to be an extremely beautiful lady and her beauty and qualities made Bhimdev Chalukya fall madly in love with her. The same story is mentioned in Rasmala.
In Prithviraja Raso, it's mentioned that Bhimdev Chalukya was madly in love with her and demanded her from her family despite him being married to Icchini's sister named Mandodari. Her father Salakha and her brother Jaitsi refused the demand and married her off to Prithviraja Chauhan. She is praised in Prithviraja Raso for being highly devoted, loyal, chaste and loving wife of Prithviraja Chauhan. She was the one who is called as his chosen wife. Her character somehow matches with the Kashibai of Bajirao- Mastani movie in Prithviraja Raso.
It's alleged that she was mother of Govindraja and when Prithviraj was captured she donned a warrior’s dress and went to rescue him but got martyred. This story is alleged only and not mentioned in Prithviraja Raso so it's authenticity is highly doubtful.
The murder of Kaimas happened in her palace when she saw that he was visiting Karnataki, his concubine. The same story is mentioned in Kanhadade Prabandha but there the queen was Padmavati, daughter of Palanasi, brother of Dharavarsha and in it she was the main queen of Prithviraj Chauhan.
Her character was also briefly shown in Sony TV's show on Prithviraj but only pre leap and after leap she wasn't introduced again to glorify the love story with Sanyogita. She was engaged with Prithviraj in the serial yet she was blatantly cheated on and then her character stopped getting even mentions. Quite unfair to the real queen who allegedly died in the battlefield who just wanted to rescue her husband and stop Jauhar of her co-wives.
Daughter of Nahar Rai Parihar
Nahar Rai Parihar, the King of Mandovar seeing the handsome Prithviraj and his qualities decided to marry off his daughter to him but he later told Someshwar that their family wasn't equal to his. This led anger among Prithviraj and his warriors and they attacked Mandovar in which Nahar Rai fought bravely but got defeated. Then he surrendered and happily married off his daughter to him. The daughter of Nahar Rai was the first wife of Prithviraja Chauhan. Her mention is not much in Prithviraja Raso. If the local folklore of Rajkumari Bela is indeed true, her mother would either be her or Icchini because these two women were his first two wives and would have marriageable daughter by the time of Mahoba war.
Pundhirni
The daughter of Chandra Pundhir said to be Chandravati or Pundhirni was the third wife of Prithviraja Chauhan. After an year of happy marriage with Icchini, he met Pundhirni, daughter of his Samanta named Chandra Pundhir and fell in love with her beauty. He proposed marriage with her and Chandra Pundhir very gladly accepted it. They got married to each other without any obstacles. It's either her or Dahimi (daughter of Dahim Rai and sister of Chamunda Rai Dahima) gave birth to his Crown Prince named Rainsi Chauhan or Rain Kunwar.
Dahimi
Dahimi was the fourth wife of Prithviraja Chauhan and she was daughter of his Samanta Dahim Rai and she was sister of Chamund Rai Dahima. She was mother of Kunwar Rainsi, Crown Prince of Prithviraj Chauhan. In some verses, his mother is called Pundhirni but most likely Rainsi's mother was Dahimi.
Padmavati
Padmavati was the princess of Samudrashikhar Garh and she was daughter of Kunwar Padmasena. She was promised in marriage to King Kumodmani of Kumaon but she fell in love with Prithviraj Chauhan and desired to marry him. Before she could get married she wrote a letter to Prithviraja to come to Shiv Temple and abduct her. She with heavy heart went to Shiva temple to pray and Prithviraj came there and she was very happy. He took her away and the army of Samudrashikhar Garh followed and fought with them but Prithviraj Chauhan defeated them and then he brought Padmavati to his place and they got married. The war with Chandelas of Mahoba happened after marriage with Padmavati in Prithviraja Raso.
Shashivrata
Shashivrata was the Princess of Yadavas of Devagiri and she was extremely beautiful. She used to study at the home of widow of Ananda Chand Khatri and it proves that princesses at that time used to be educated and tutored well by their families. She fell in love with Prithviraj Chauhan. Once a dramatist (Nat) visited court of Prithviraj Chauhan and praised the beauty of Shashivrata saying he was employed by the royals of Devagiri. Prithviraja fell in love with her description.
Shashivrata was already betrothed to somebody else (Virchand or Jaichand or Kamdhwajj) but she wanted to marry Prithviraj. To get Shashivrata ,he went to Devagiri and took her from Shiv Temple and she too consented for it. The story is quite similar to his marriage with Padmavati.
The armies fought Prithviraj but again he defeated them and married Shashivrata.
Indravati
The daughter of Raja Bhim Parmar of Ujjain was betrothed to Prithviraja Chauhan but he had to go and aid his brother in law in a war. Prithviraja was supposed to marry her but due to the war he sent Panjjun Rai with his sword to marry Indravati with his sword and bring her to the palace. The King of Ujjain felt it insulting and declined the marriage. Chandra Bardai tried to reason with him and after a petty skirmish between them and also seeing Indravati wanting to marry Prithviraj, Bhim Parmar agreed for the marriage and he married off Indravati to the sword of Prithviraj and Pannjun Rai presented Indravati to Prithviraj and he gladly made Indravati his queen.
Her character was briefly shown in Star Plus' show on Prithviraj but to glorify Sanyogita, Indravati was unnecessarily made bland , petty and jealous and then her character suddenly vanished without any conclusion. It's quite unfair to demean a queen to glorify another queen who isn't even glorified in the real source.
Princess of Kangra
Prithviraja attacked King Bhan Bhoti of Kangra and successfully defeated him. The King married off his daughter to Prithviraj Chauhan.
Hansavati
Hansavati, daughter of Raja Bhan Rai and Princess of Ranthambore was one of the wives of Prithviraj Chauhan. King of Chanderi named Panchaeen fell in love with her but her father refused to marry her to him. So, he attacked Bhan Rai. He asked for help from Samar Singh (Rawal of Chittor) and Prithviraja Chauhan and the alliance of the brothers in law with Bhan Rai defeated Panchaeen. He offered the hand of Hansavati in marriage to Prithviraja Chauhan and he gladly married Hansavati.
Govindraj Chauhan, the son of Prithviraj Chauhan and allegedly Icchini had gone to Ransthambpura (Ranthambore) when ousted by Hariraj Chauhan due to being Vassal of Aibak.
Sanyogita
Sanyogita is the most famous wife of Prithviraja Chauhan. She was daughter of Maharaja Jaichand of Kanyakubja. Her name is Kantimati in Surjan Charita. She fell in love with Prithviraj Chauhan while studying in the school of Madan Brahmni and he too fell in love with her when he heard about her beauty from a visitor at his court. They both were pining for each other. Jaichand after unsuccessfully doing Rajasuya Yajna decided to do her Swayamvar but she garlanded statue of Prithviraj Chauhan. She was confined to her palace near Ganges river by Jaichand. Prithviraja even when warned by his queens and Chandra Bardai visited Kannauj in disguise and met Sanyogita in her palace. On her request they did Gandharva Vivah and then on advice of Kanha Chauhan they eloped together on his horse. His main and very capable warriors died in this war. Jaichand ultimately accepted the marriage and sent gifts and captured injured soldiers of Prithviraj Chauhan back to Delhi.
Prithviraja Raso mentions that he became obsessed with her and gave her half of his throne to her. He spent day and night in her palace and left administration on his courtiers. His Chief Queen Icchini became highly angry and full of grief due to his neglect and decided to leave him forever. When he saw her leaving he asked about her grief and when he got to know the reason, he said sweet words to her and begged her to stay with him. Icchini out of her love and devotion towards Prithviraj stayed back and he felt hurt for giving pain to Icchini whom he loved very much.
When Sanyogita heard that Prithviraj was captured, she died immediately as she couldn't survive listening to this painful news.
Source: Prithviraja Raso
The source is an interpolated one and probably the marriage stories are exaggerated and more poetic versions of just normal marital alliances kings used to do that time. Other queens like Kurambhi, etc. are also mentioned.