Varghese is a name that comes from Kerala, India. It is a given (ie, first) name. With the local practice of using the father's first name as the child's last name, it has become a last name as well. Take my own name as an example: Raju is my name and Varghese is my dad's name. When I was born and a name had to be registered, the full name was Raju Varghese. Wikipedia has extensive information on names in various parts of the world including India.
Varghese is a Christian name. About 30% of Kerala's population is Christian. The Kerala Christians believe that they were converted to Christianity by St. Thomas (the unbeliever), one of the twelve apostles of Christ. St. Thomas came to South India after Christ's death. Kerala was in close contact with the Chinese and Romans long before that seminal event. For example, persecuted Jews from modern-day Iran settled down here in the B.C's. So ... where was I ... errrr... Yes, Varghese is a common Christian name in Kerala and the root of the name is what I will expound on next.
I'll let the cat out of the bag right here: the name Varghese comes from the same root as the name George. That probably needs some explanation as the link is not obvious. The root is probably Geewargis and comes from the region in and around Turkey. I say probably because I do not have historical evidence to prove it. St. George came from this region and the dragon that he reputedly slayed must have lurked in a cave here as well. As the name spread to Greece and Macedonia it became Georgios from which Georges and George are derived. The spreading of the culture, and ultimately, the name to the East resulted in the following: Geevargis, Vargis, Varghese, Varkey, etc. In Kerala, the following names are quite common: Varghese, Verghese, Vargis, Vergis, Varkey, Geevarghese. The Christians of Turkey still use the name Gewargis.
A common mistake that people make when initially confronted with name Varghese is that they think it's Italian. After all the Borghese family of Italy was quite famous (or infamous, depending on which side you find yourself). Varghese has nothing to do with Borghese even though they sound similar. Actually, they do not sound similar but one would be led to believe that they do from the spelling. Varghese is pronounced Vär gees' and not Vär geseh.
Variations of the name George from various parts of the world: