the man who first decided to call Andaman was Italian and the name stuck forever?

Where’d you pick up this tidbit of information? Far as I know, “Andaman” derives from “Handuman”, the Malay word for the Hindu god “Hanuman”. Which Italian are you talking about?

No Indian states have British or Italian names. All are local. You could argue that “Nagaland” has “land” in it, which is English, but Nagaland is very new - it was only created in 1963, long after English had become an official language under the Indian constitution.

Indian place names vary depending on region and the language spoken there. Bengali in the east, Tamil, Telugu, Malayalam in the south, mostly Hindi or Urdu in the north, etc.

Like in most countries, place names have some historical relevance in India. Some could simply belong to the “since times immemorial” category, meaning that’s what it’s been called for as long as anybody can remember, nobody knows why. Other place names have some recognizable etymology reflecting their origin. For example, Punjab is “panj” plus “ab” meaning five rivers. Or Uttar Pradesh, meaning Northern Province, Madhya Pradesh meaning Middle Province, etc.

Some towns may be named after the people or tribe who used to live there (or still do), like “Bhilwara” for the Bhil people, “Mizoram” for the Mizo people, etc. Some places are named after their founders, and usually end in “abad”, meaning “settled or populated by”. For example, "Hyderabad", "Moradabad", "Faisalabad", presumably founded by Hyder, Morad, or Faisal.

Some places have a military association, being named after fortifications or castles. They usually have names ending in “garh” which means a fort. Like Aligarh, Junagarh. Others may have names ending in “nagar” or “shahar” (town in Hindi and Urdu, respectively), like Gandhinagar, Muzzafarnagar, Bulandshahar. Or in “pur”, which also means place or habitation, like Sultanpur, Nagpur, Kanpur, Bijapur. Some places reflect their status as waystations on some ancient travel route. These usually end with words like “serai”, which means a caravan stop. Like Mughal Serai, Yusuf Serai, Jia Serai.

These are examples of north Indian naming conventions, which as I said, mostly come from Hindi and Urdu, plus regional languages like Punjabi, Haryanvi, etc. Other parts of the country have their own languages and naming conventions.

British names are sometimes found, but they are not common. For example, Dalhousie in India, or Abbotabad in Pakistan. More common are British spellings on Indian names. The Brits couldn’t pronounce local names so they had their own unique spellings based on how they pronounced them. Much of the English literature uses these British spellings, though they have been slowly replaced by more accurate Indian spellings. For example Calcutta to Kolkota, Bangalore to Bengaluru, Cochin to Kochi, Trivandrum to Thiruvananthapuram, etc. Again, these are Indian names, not British. They just had different spellings because the Brits pronounced them differently.

There is some smaller amount of Dutch and Portuguese influence in parts, but I’m not aware of any Italian influence.