Whatever the specific version told, Ganesha's origin narrative consistently establishes him as the son of Shiva and Parvati and explains his most recognizable physical feature, and it also typically explains why he is invoked first before any significant undertaking: accounts describe Shiva or the gods more broadly granting Ganesha the status of first worship, Prathama Puja, and the role of remover of obstacles, Vighnaharta, either as compensation for the trauma of his beheading or as recognition of a subsequent contest of wisdom he won against his brother Kartikeya.
Hindu tradition generally treats the variation across different tellings of Ganesha's birth as an accepted feature of Puranic literature rather than a problem requiring resolution, with different regional and sectarian communities emphasizing whichever version circulates most strongly in their own local tradition without treating other versions as thereby false.
Ganesh Chaturthi, the major festival commemorating Ganesha, is celebrated with particular intensity in Maharashtra and increasingly across India and the global Hindu diaspora, involving the installation of clay images of Ganesha in homes and elaborate public pavilions for several days of worship, followed by a ceremonial immersion of the images in water, a practice that has itself become a significant point of contemporary environmental discussion given the materials modern images are sometimes made from.