The manipulation of natural energy is called Senjutsu which allows sage mode.
Idk if anybody noticed but Senju and Senjutsu are spelled almost the same.
To me this could either be two possibilities.
1 the senju clan was adept at Senjutsu and was named after it.
senjutsu and the senju clan have more than just a name that is similar.
The senju clan is descendent of the sages younger son.
Having inherited the sages body he was probably capable of sage mode.
Due to him and his descendents being adept in Senjutsu they were name the Senju clan of the forest. (forest having to due with nature)
Or two it could just be a coincidence and im just over thinking things.
leave your opinion please. Dont just read. thank you.