These are Hindu Brahmins who affiliate either with the Gautam gotra and/or Gautam Dharmasutra and have their last name as Gautam.
Etymology
The name Gautam (Sanskrit: गौतम, a vrddhi patronymic of Gotama and also transliterated as Gautama or Gauthama) is one of the ancient Indian names and is derived from the Sanskrit roots गः gaḥ and तम tama. Tama means “darkness” and gaḥ means inter alia "bright light". Together they indicate the one, who dispels darkness (i.e., ignorance) by his brilliance (i.e., spiritual knowledge).
Generally some Brahmins who affiliate either with the Gautam gotra and/or Gautam Dharmasutra in the states of Haryana, Rajasthan, Western Uttar Pradesh, Himachal Pradesh, Karnataka and Tamilnadu write the last name as Gautam.