The person who feels god in his heart may be referring to Yahweh, Vishnu, or any number of beings. How would you determine that this feeling is Jesus, and not Brahma?
There is a saying that love and hate are two sides of the same coin.
But to answer your question, that person would very likely tell you which God they feel in their heart and why. Or maybe they couldn't. Like the complex emotions we've touched on, they just know they feel God.