Lord Ganesha manifests himself through various events in various cycles of creation. One time Goddess Parvati while playing prepared a doll while playing and gave it the shape of an elephant head. She threw that doll to Ganga and that doll Grew in size and both Parvati and Ganga addressed him as "son". Thus, Ganesha is also called Gangeya and hence the name Dvaimatura. This story is present in Padma Purana, Shristi Khanda chapter 43:
सुरक्तहृदयो देव्या विजहार भगाक्षिहा ||
ततो बहुतिथे काले पुत्रनाम्ना गिरेः सुता |
सखीभिः सहिता क्रीडां चक्रे कृत्रिम पुत्रकैः ||
कदाचिद्गंधतैलेन गात्रमभ्यज्य शैलजा |
चूर्णैरुद्वर्तयामास मलेनापूरितां तनुम् ||
तदुद्वर्त्तनकं गृह्य नरं चक्रे गजाननम् |
पुरुषं क्रीडती देवी तच्चाप्यक्षिपदंभसि ||
जाह्नव्या शिवया सख्या ततः सोभूद्बृहत्तनुः |
कायेनातिविशालेन जगदापूरयत्तदा ||
पुत्रेत्युवाच तं देवी पुत्रेत्यूचे च जाह्नवी |
गांगेय इति देवैस्तु पूजितोऽभूद्गजाननः ||
विनायकाधिपत्यं च ददावस्य पितामहः | (Padma Purana 1.43)
He, the destroyer of the eyes of Bhaga, with his
heart that was very much attached, sported with the respectable
lady (viz. Parvati) in charming city-gardens and secluded
thickets. When a long time (like this) passed, the Mountain's daughter played with artificial sons (i.e. dolls) with her
friends (in) a game called 'Son'. Sometime the Mountain's
daughter anointed her body with fragrant oil and rubbed and
cleaned it which was filled (i.e. covered) with dirt. Taking those unguents used for rubbing and cleaning the body, she prepared a human (shape) having an elephant's face. The respectable lady (i.e. Parvati) while playing, once
threw that human (form) into the water of the auspicious
friendly Ganges. Then that (form) turned into one having a
big body (i.e. increased in size).With his very vast body he filled the world. The respectable lady ( ie. Parvati) addressed him 'O son'; and Janhavi (i.e. Ganga) also called him 'O son'. That form having the face of an elephant, was worshipped by the gods as Gangeya (i.e. the son of Ganga) ; and the grandsire, gave him supremacy as Vinayaka (Vinayakadhipatyam).