My name is

So you are walking along the street and you see someone you want to meet. You walk over to him or her and say, χαίρειν. τὸ ὄνομα μου ἐστιν ...

Greek would not just say ὄνομα μου ἐστιν. They would put the article before ὄνομα. But we don't talk like that, so when we translate we say "My name is ...," not, "The my name is ...."