My name is David

My actual name is "Bill" -- I am the Professor. "Bill" is not a Greek name, so for the sake of illustration I will use the name ὁ Δαυίδ for myself.

If I were to see you, and especially if I did not know you, I would come across the street and say, χαίρειν. τὸ ὄνομα μου ἐστιν ὁ Δαυίδ.

Using your new Greek name, turn to the person next to you and say,
"Hi. My name is ..." and supply your Greek name.