The 7th month, is it Ethanim or Tishrei. Are they same?

Yes, the real name is Etanim. From 1 Kings 8:2. Not all the months are given names but this one was. Tishrei is a Syrian/Babylonian name that later replaced the real name. Better to call it as the Torah called it! 

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According to Merriam Webster, Ethanim is the 7th month of the ancient Hebrew calendar corresponding to Tishri

https://www.merriam-webster.com/dictionary/Ethanim