Boogerman : The NWT wrongly/falsely attributes God's name (Jehovah) to the meaning of Hebrews 13:15
As this thread is about translation it should be noted that the NWT does not attribute any meaning to "his name" in Hebrews 13:15. It just reads "... the fruit of lips which makes public declaration to his name."
The Watchtower article with which you disagree indicates it is referring to God's name, but it has nothing to do with translation. However, since vs 15 talks about offering God a sacrifice of praise, and vs 16 says that God is well-pleased with such sacrifices, it is quite reasonable to conclude that the sacrifice is made "to [God's] name".