Is God eponymous

Answer 1

No, but obviously He is with His Name. We do not know the actual name of God as the Israelis only recorded the consonants: YHWH, but it is commonly referred to as Yahweh which is an ancient Hebrew verb tense of "To be", then when God gave His name, He was basically saying I am "I AM".

Answer 2

The Biblical Answer is that God will accept that his worshippers be known by his name as long as they live up to it:

Acts 15:13-18 (NIV) "When they finished, James spoke up. “Brothers,” he said, “listen to me. Simon has described to us how God first intervened to choose a people for his name from the Gentiles. The words of the prophets are in agreement with this, as it is written: 'After this I will return and rebuild David’s fallen tent. Its ruins I will rebuild, and I will restore it, that the rest of mankind may seek the Lord, even all the Gentiles who bear my name, says the Lord, who does these things’ - things known from long ago." (James was quoting from Amos 9:11,12)

There was a time when the Jews would use God's name in their every day speech, and even mention the name when they greeted someone. Possibly in the form of "Yahweh (YHWH) be with you" or "Praised be Yahweh" or something of that nature. This was to identify them as worshippers of Yahweh. In fact, many Hebrew names in The Bible actually contain a form of the divine name in them and this was apparently acceptable to God, as long as the person lived up to the designation.

Although in Jewish tradition the name of God stopped being used, the Bible repeatedly says that God wants his worshippers to use it and proclaim it. The most common rendering of the divine name into English is Jehovah as it was translated centuries ago. The name was made mainstream by the original King James Bible where it renders the name 4 times, and the original American Standard Version where it's rendered well over 100 times. More recently, Jehovah's Witnesses and a few other Christian denominations emphasize the use of God's name. There is even a new "Divine Name King James Bible" that was recently published that contains the rendering "Jehovah" about 7000 times.

The rendering Jehovah may not be the exact pronunciation or rendering, but it does follow in line with the standard of English translation of Hebrew names. The Hebrew letters YHWH translate to JHVH into English. Some of the names of people in the Bible whom had a portion of the divine name contained in their own name are: Jehu, Jehoahaz, Jehoash, Jehohanan, Jehoiada Jehoiachin, and Jehoshaphat to name just a few. Of course, some of the persons who had the divine name within their own name did not live up to the designation.