First of all please don't say "a trans". Second, if you are born in the body of a certain sex, but you identify as the other sex (that is, your brain is actually wired like the brain of the sex you identify with, but your body was developed according to the other sex, this is all due to hormonal imbalance in the womb), then you are transgender. Whether or not you get any operation (there is more than one, so "the operation" is nothing) does not have any effect on the term transgender. Adding to that your wording was pretty shitty. Your hypothetical trans person is getting a "sex change" but you still call them a man. Trans people prefer to be called by their actual gender, that is the gender they identify with. So saying "he" and "a man" are untrue. Because they are not a man if they identify as a female (I'm guessing that is your hypothetical). Also, you could have just googled the definition of "being transgender".