It was interesting to see New Zealand saving a Test against India with the last-wicket pair being of Indian origin. While AY Patel was born in Bombay in 1988, R Ravindra was born in New Zealand in 1999. There are a few others with Indian-sounding names who were born in New Zealand.
Here we attempt to enumerate the members of 2 categories
1. Born in India (including pre-partition India):
FT Badcock (Abbottabad, 1897)-presumably British-7 Tests
AY Patel (Bombay, 1988)-10
N Puna (Surat, 1929)-3
JA Raval (Gujarat, 1988)-24
IS Sodhi (Ludhiana, 1992)-17
2. Indian-sounding name, not born in India:
DN Patel (Kenya, 1958)-37
JS Patel (New Zealand, 1980)-24
R Ravindra (New Zealand, 1999)-1
Those of Gujarati origin just outnumber the others. Badcock, Sodhi and Ravindra are the exceptions.
Among these players, it was Nairobi-born Dipak Patel who played the most Tests for New Zealand. He was a member of the 99 Club, and finished with 1200 runs and 75 wickets. Next are JA Raval and JS Patel who played 24 Tests each.