However, we should broaden our knowledge and develop our thinking, and we should not copy what others say. We should understand the source and origin of "tengen". The term "tengen" was widely used in other fields in ancient China, but it is not a proprietary traditional WeiQi term, so it cannot directly represent the traditional Chinese WeiQi culture.
It depends what you mean by "we". If you mean Chinese people, what you say may be fine, although more accurately you should in that case say tianyuan is the "false" term.
Almost all go players outside China use Japanese, and the related Korean, rules. Almost all (Korea excepted) use Japanese terminology.
There is absolutely nothing wrong with Japanese using the term tengen. It was not, and never has been, tianyuan in Japanese.
The Japanese term was invented in Japan by a Japanese person for a game using Japanese rules, and was read in the Japanese way (Sino-Japanese if you prefer, but that was still Japanese).
The inventor, furthermore, was a distinguished go player: Originally Yasui Santetsu (1639 ~ 1715), son of Yasui I. He became better known as a scholar and astronomer under the name Shibukawa Sukezaemon Shunkai, or more simply Shibukawa Shunkai, although recent research suggests it was meant to be read Shibukawa Harumi.
The go part of thje story is that, in 1657, under the guardianship of Yasui Sanchi, he began to receive an official stipend and, after being appointed as the family heir in 1659, he began to play in Castle Games. According to Honinbo Dosaku he was 7-dan. He was also a distinguished Confucian scholar and the foremost expert of his time on astronomy, at which he became expert by studying the latest Chinese books based on imported European principles, and by making his own astronomical observations. A revised version of the calendar (the first by a Japanese) is due to him, at imperial request, and because of his involvement with this from 1683 he ceased playing Castle Games as Yasui Santetsu II. His new Jokyo era calendar was issued in 1684 and was used for 70 years. His reward was to be appointed by the shogunate to the Astronomical Institute (Tenmonkata) and it was in that capacity he changed his name to Shibukawa (the original name of the Yasui family) in 1702 and retired in lunar 1711-XII. He published many books on astronomy. His astronomy inspired a famous Castle Game against Dosaku in 1670 (GoGoD 1670-11-29a) when he played first move on the centre point (he lost by 9 points). It is from this that it is widely accepted (though not proven) that tengen as a go term may have become popular.
Furthermore, he was the subject of a 2010 book by Ubukata To,
Tenchi Meisatsu (Insights into the Universe), partly about his life as ago player though mainly as a calendar maker). This won the Yoshikawa Eiji Literature Prize for New Writers and the Booksellers Prize (Honya Taisho). It has been made into a film. No doubt connected with this, he was an early inductee into the Nihon Ki-in Hall of Fame in 2012.
In short, Shibukawa and tengen are an important part of Japanese history in general. If you wish to make the point (a valid one) that people outside China should know the history of go in China better, you have to accept also that people within China ought to know the history of Japan better. This extends beyond go. Shibukawa was a Confucian scholar. But Confucianism in Japan was not the same as in China. In China, Confucianism is predicated on the Emperor having the Mandate of Heaven (in practice, the will of the people). In Japan, as defined by the Taiho Code of 701, which was a code drawn up explicitly to introduce Confucian ethics into Japan, the Emperor ruled by birthright (as with our new King Charles III). Are we to say Japanese ethics are false?
None of this should be turned into a nationalist "my dad is bigger than your dad" game.
All the above, also explains why nearly all of us in the west say "go" and not weiqi, while happily conceding go probably originated in China. For us, go is not a "false" name.
But what is a false name is taichi. It (太极) should of course by taiji. The commonest rendering of that in English seems to be Great Ultimate, though Supreme Pole has some adherents.