yes sir we can have any name including Bharti but that certain gentleman was interested in getting know the word '
Bhartiya' or '
Bharatiya' which is about the nationality of Indian, hindi of word 'Indian'. like, in english we call a citizen of India as Indian, and in hindi we call him/her Hindustani or Bhartiya because we call India as Hindustan or mainly 'Bharat' in hindi language.
in fact, in english we would write it as Bharatiy but now Lord Ram is written in english as Rama, Sri Krishn is written as Krishna, Gautam Buddh as Buddha, so, we would write hindi of Indian as Bhartiya or Bharatiya, I think