I'm looking for a word to name or call a person who's sitting next to me and I mean it in general.
A person who sits next to you on a bus, airplane, etc.
You can use the word neighbour to describe somebody sitting next to you on a plane or bus.
I chatted with my neighbour on the flight to New York
If you wanted to be completely clear that you were not talking about the man who lives in the house next to yours, you could say:
I chatted with the man in the neighbouring seat.
This is a very uncommon word, but it is nonetheless a word in English.
It is a word that has minimal data on Merriam-Webster, but nonetheless, it has a place in their dictionary.
Also, to prove the existance and usage of this word, check out what Google Ngram has to say.
It should be a variation of the commonly used word 'Bystander'.