“I came to know” is an expression in English that often describes the manner of how(or from whom) you discover something. “Come to Know” is not common as the expression is usually used in the past.
I came to know about him through an old acquaintance of mine.
Came to Know
“Came to know” is an old-fashioned/literary way of saying “to discover” or “to learn about” something. The phrase is not very common to use in Modern English but it can still be found in spoken and written English.
We often use “came to know” when we want to show that the manner of discovery was somehow interesting(not just the discovery itself).
I came to know about Freud through an Austrian psychologist who claimed to be his grandson.
In the example above the discovery of the books of Sigmund Freud is not that interesting but the person who told you about him is more interesting.
Come to Know?
“Came to know” is usually used in the past tense so “Come to know” is only possible in the interrogative past form.
How did you come to know about string theory?
This is not very common as you are implying that the person has an interesting story about how they learned about a certain topic when you don’t really know the full story.