Buddhi, Siddhi and Riddhi
The Mahapuranas and the Upapuranas mention that Lord Ganesha was married with Buddhi, Siddhi, and Riddhi. Buddhi represents wisdom, Siddhi signifies spiritual power and Riddhi represents prosperity. His wives are depicted in human forms. They appear on either side the elephant-headed Hindu god. The descriptions of Siddhi and Buddhi are provided in the Mudgala Purana and the Ganesha Purana which are devoted exclusively to the Lord. These religious texts mention His consorts as an intrinsic part of Lord Ganesha.
The Ganesha Purana mentions that once Lord Brahma performed a ritual to worship Ganesha (Vinayaka). During the ritual, Lord Ganesha made Buddhi and Siddhi appear so that Lord Brahma could offer them to the elephant-faced deity. He accepted them as offerings and made them His wives. Another version of the incident is also mention in the Ganesha Purana. The legend states that all the gods were offering various gifts to Lord Ganesha. Lord Brahma presented Ganesha with Siddhi and Buddhi who were born from the mind of Brahma.
The Indian religious scriptures mention that Buddhi and Siddhi or Siddhi and Riddhi were the two wives of Lord Ganesha. In several temples throughout India, the sculptures of the deity are depicted with both Siddhi and Buddhi. One of the goddesses is seated over the left thigh of Ganesha while the goddess on the right is generally depicted in a standing posture. In the Ganesha Temple at Morgaon, the sanctum includes an image of Lord Ganesha. Siddhi and Buddhi are shown standing on the right side and left side of the idol. The two spouses of the Lord are identified as Siddhi and Riddhi in North India.
The Shiva Purana tells that after Lord Ganesha and Lord Kartikeya competed against each other to achieve the right to marry Buddhi and Siddhi, the two daughters of Prajapati. Lord Shiva and Goddess Parvati decided whoever revolves around the world and reaches back first would be married. Lord Kartikeya immediately mounted his peacock and began his journey. But Lord Ganesha used his intellect and wisdom and requested Lord Shiva and Goddess Parvati to sit together. Then Ganesha went around his parents with utmost devotion and demanded to be married immediately. When Shiva said that he did not go around the world, Ganesha replied that he revolved around his parents as they parents represent the entire world. Thus He was declared the winner.
The legend also mentions that the Lord had 2 divine sons, namely Kshema (meaning prosperity) from Siddhi; and Labha (meaning acquisition) who was born to Buddhi. In the North Indian version, the sons of Ganesha are known as Shubha (meaning auspiciousness) and Labha. The Ganesha Purana mentions that Lord Ganesha is also known as Rddhi-Siddhi-Pravardhana, meaning the enhancer of material and spiritual success. Moreover according to the Matsya Purana, Ganesha is considered as the owner of Buddhi (wisdom) and Riddhi (prosperity).
Vinayaki or Ganesani is considered as female Ganesha and is believed to be the Mistress of Obstacles. Hence She is assumed to be Shakti, the consort of Ganesha. Vinayaki is depicted with an elephant head and is primarily worshipped by Buddhists and Jains. The Hindu religious texts provide little information about the goddess. As the female deity has elephantine features like Lord Ganesha, She is associated with the Remover of Obstacles. Vinayaki also has the ability to remove obstacles like Lord Ganesha. The Devi Purana describes Vinayaki as the wife or Shakti of Lord Ganesha.
Lakshmi and Saraswati
Lord Ganesha is usually worshipped together with his wives Goddess Saraswati and Goddess Lakshmi, for the acquisition of material welfare and prosperity. Lord Ganesha and Goddess Lakshmi control Riddhi (material welfare) and Siddhi (spiritual prosperity); and Goddess Saraswati and Lord Ganesha are considered to be the gods of Buddhi (intellect).
In West Bengal, Kola Bou is worshipped during the festival of Durga Puja. Lord Ganesha is associated with a banana tree during the rituals. The tree is worshipped as a Goddess throughout the festival. Kola Bou is adorned with a saree and the leaves are smeared with vermilion. The Tree Goddess is then worshipped incense sticks, sandalwood paste and flowers. She is installed on the right side of Lord Ganesha during the rituals.
It is also believed that Kola Bou is an incarnation of Goddess Durga (a form of Parvati) and is not considered as the consort of Ganesha.