Sort of. Let's examine the key passage below.
Ex 3:13 Moses said to God, “Suppose I go to the Israelites and say to them, ‘The God of your fathers has sent me to you,’ and they ask me, ‘What is his name?’ Then what shall I tell them?”
14 God said to Moses, “I am who I am. This is what you are to say to the Israelites: ‘I am has sent me to you.’”
15 God also said to Moses, “Say to the Israelites, ‘The LORD [Hebrew YHWH], the God of your fathers—the God of Abraham, the God of Isaac and the God of Jacob—has sent me to you.’
“This is my name forever,
the name you shall call me
from generation to generation.
People have been using the tetragrammaton YHWH since Adam and Eve (Gen 4:1). Yet despite that, Moses asked God what his name was. That's because YHWH wasn't really a name like "Tom" or "Jerry". (The surrounding nations had names for their gods like Chemosh, Molech and Dagon.) It was interpreted more like "Lord" which is how it was translated into the NT (ref Ac 2:34-35; Ps 110:1; the Greek word for "lord" is "kyrios"). (Note all other Hebrew names were transliterated into the NT, thus for example Yeshua became "Iesous" in Greek or in English "Jesus", so the the non-transliteration appears intentional on the HS' part.)
Even "I am" is somewhat cryptic. It's not really a name either. It appears basically God told Moses if you want a "name" go with "I am", but continue using YHWH as a "name" like you've been doing, even though you really don't think of it as a name. Jesus used the "name" "I am" as his name a couple of time when addressed some Jews (Jn 8:24,58). But because it's not a common "name", they didn't pick up on that until the second time when he also explained that he existed before Abraham. Then they tried to stone him for blasphemy, calling himself God.
It should also be noted that it never was God's idea to even come up with "I am". Had Moses not asked the question, possibly we'd never even know that as a "name".
Most Christians just follow Jesus' example of how to address God:
"Our Father in heaven" (Mt 6:9).
The only ones going way overboard and overthinking the whole issue are the JWs. They've gone so far as to even add "Jehovah" to their own version of the NT, even though no Greek manuscript (from which we translate the NT) has that term.