You will not find any evidence of gods name in the new testament because there has never been found any text with the name in it. As far as the yhwh its only an assumption or conspiracy that this is how the jews spelled gods name after they returned from Babylon. There is some evidence from places like elphantine egypt that gods name was spelled similiar to yhwh, when quotes were found stating to Yw and his Ashurah. A few other places the spelling of Yh or Yhw has thought to be the spelling of the Hebrew gods name but thats about all your going to find except in early old testament scriptures where the names of El and his different discriptions are used. El-shaddai, Eloyn, etc.
When ones goes out side of the bible one can find more documents that support the name of the Hebrew god, like the writtings found at Ugarit.