15th Regiment of Madras Native Infantry

Known as 15th Regiment of Madras Native Infantry in the Madras Army
Known as 75th Carnatic Infantry in the Indian Army

Chronology

1776 raised as 15th Carnatic Battalion from 2nd, 6th and 12th Carnatic Battalions
1784 became 15th Madras Battalion
1796 became 2nd Battalion, 4th Madras Native Infantry
1824 became 15th Regiment of Madras Native Infantry
1885 became 15th Madras Infantry
1903 became 75th Carnatic Infantry
1922 became 2nd/3rd Madras Regiment
1926 disbanded
1940 re-formed.

The Madras Regiment, 1758-1958 by E.G. Phythian-Adams 1958. Available at the British Library UIN: BLL01012507899 .

Madras Regiment Wikipedia
3rd Madras Regiment Wikipedia
75th Carnatic Infantry British Empire website
2nd Battalion, The Madras Regiment madrasregiment.org
Page 53 Valour and Sacrifice: Famous Regiments of the Indian Army by Gautam Sharma Google Books
"The British Campaign in Aden, 1914-1918" by Mark Connelly Journal of the Centre for First World War Studies Vol. 1, No. 3, 2005. pages 65-96, now an archived webpage. Includes brief mention of the 75/Carnatics.

Madras Infantry 1748-1943 by Lt.-Col. E G Phythian-Adams, late 3rd Madras Regiment published 1943 is available Archive.org, mirror from Digital Library of India. Two files are available, barcode 4990010018885 seems a more complete copy, File 1, (File 2)
The Madras Soldier 1746-1946 by Lt.-Col. E G Phythian-Adams. Revised and enlarged edition 1947 Archive.org.