Double quotes can be escaped like this:
string test = @"He said to me, ""Hello World"". How are you?";
But this involves adding character "
to the string. Is there a C# function or other method to escape double quotes so that no changing in string is required?
No.
Either use verbatim string literals as you have, or escape the "
using backslash.
string test = "He said to me, \"Hello World\" . How are you?";
The string has not changed in either case - there is a single escaped "
in it. This is just a way to tell C# that the character is part of the string and not a string terminator.