Which gotra has vandiyar
No
is there a gotra by name shiva gotra
vishnu
(Shiva) gotra , and nandi surname is a kayastha (kshatriya) .
Yes debnath bhahmins are of higher cast , they origin from "shiva" so they are called "rudraj brahmin" . Their gotra is called :"shiva gotra ". All human being originated from kashyap hrishi, but debnath are from lord shiva not from any hrishi but directly from shiva. "Brahmins are immigrants & not ethnic indians. They were cunning, wicked & one of the shameful humans in the world, always intended to implement Divide & Rule policy" - B.R.Ambedkar
Shiva Gordon's birth name is Shiva Bagheri.
Shiva Thejus's birth name is Shiva Teja.
Shiva Rose's birth name is Shiva Rose Gharibafshar.
Vignesh Shiva's birth name is Vigneshwar S.
Shiva Gered's birth name is Siva Gerede.
Shiva's abode is Mount Kailas.
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.
Bhootnath is an appellation of Lord Shiva.