Wikipedia
The name Gautam (also transliterated as Gautama or Gauthama and a vrddhi patronymic of Gotama) is one of the ancient Indian names and is derived from the Sanskrit roots "gŐ(गः)" and "tama (तम)". "Tama" means "darkness" and "gŐ" means inter alia "bright light". Together, they indicate the one, who dispels darkness (ignorance) by his brilliance (spiritual knowledge).
The name Gautam is a masculine name. The feminine counterpart is known as Gautami.
Credited to the great sage, a descendent of Mahaṛṣi Āngira, the name Gautam might have come into limelight first during the Vedic period. There were several great and renowned rishis, who belonged to the Gautam gotra but all of them assumed the generic name of Gautam only. The name had a conjuring effect by virtue of the merits of the great Vedic rishi Gautam and his illustrious descendent rishis so much so that, numerous other persons sought to assume this name in ancient times.
A Gautam gotriya Brahmin named, Indrabhuti of Gochchar village of the ancient Magadha kingdom, who became the chief disciple of Lord Mahavira, the 24th Jain Tirthankara, was called as Gautam Swami.
Siddhartha (of Buddhism) was born in the Shakya clan that belonged to the warrior ( Kṣatriya) caste. He was called as Gautama to perpetuate the name of his foster mother, Gautami for the love she bestowed on him
The current naming practices in India can be traced to the massive advent of European in India during the 18th century. Since the intractability of the Indian naming methods and their meanings confounded the Europeans, they supposedly introduced the naming method, of having first name, middle name, and surname in their urge to influence, modernize and develop the Indian system accordingly.