Is it right to call Allah by the word God..

Yes, it is. I am Christian, and when I speak to those of the Islam faith, I use "Allah" for God.

And many of the people of the Islam faith that I speak to use the word "God" for "Allah".

It is only a language issue. For people of many faiths, the terms are interchangeable, meaning The One and Only God, The Omnipotent One, The Creator, etc.