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Not all the people with same name will have same gotras. My surname is also trivedi and I am from Bhardwaj Gotra. But you might also be from different gotra as well. You should ask elders of your family they might know your gotra.
Kaushik itself is a gotra in a brahmin community.. it is one of the upper most gotra in brahmin commnity
Which gotra has vandiyar
Kashyap Gotra ( Jains ) People's kuldevta is Babaji Maharaj (place - Nitoda, Sirohi district, Rajasthan).
is there a gotra by name shiva gotra
No you cannot marry in same gotra. Its prohibited in vedas. And it also has a scientific reason yo marry in same gotra there will be a genetic disorder in offsprings.
No they can't. For that matter no two Brahmin people from two gotras having a rishi in common can marry.
Sandliya Gotra
No you can not marry her. According to Hinduism people from same gotras can not marry each other.
bhargava gotra
Manu Gotra
Gotra-Kashyap Sub Gotra- Dhanpal