One of the readers has taken pains to get a reference text in Mysuru, published in the year 1900!My gratitude to him. I am providing the communication from him
There is also a practice of assigning Vishnu Gotra to people who belong to Kshatriya Varna and Jambu Maharishi Gotra to Vaisyas.
Though it is a Brahmin Gotra,it might have been modified as a Kshatriya Gotra because of change in Profession.
Viswamitra Gotra is a Brahmin Gotra .
But when Viswamitra became a Rajarishi and gave the Gayatri Mantra to the world his Gotra became Brahmin.
This system also takes into account instances when one has more than one wife. Over a period of time name of the benefactor is also included as Gotra,as a mark of Respect.
The term Vishnu is from the Sanskrit root Jishnu
'Vishnum Jishnum Mahavishnum prabha Vishnum Maheswaram' Vishnu Sahasranama.
Jishnum means 'supporting,supportive'
As Vishnu is the Protector and supports the Universe,he is called Vishnu.