Oooh, kendo seems like it would be great fun!!!!!
Hahah, well sadly for you the Japanese common word for redwood is "Amerika Sugi" which isn't particularly interesting, although I suppose it's rather easy to pronounce
" Sequoia would be "aka sugi" (literally red cedar), and following that reasoning "sugi" is the word for cedar. Pine tree is "matsu" and is actually a common component in a lot of people's names. Some variations which may be fun for a sword name are "matsuba" which means "pine needle", or "wakamatsu" which means "young pine" and is a symbolic new year's decoration here.
Some others (because I'm having a lot of fun with this)
"Roushyou" - "old pine tree"
"matsukaze / shyoufuu" - "the sound of wind though pine trees"
"kuro matsu" - "black pine"
Oh, and "take" (pronounced "ta-ke") is the word for "bamboo", and "take no ko" the name for "bamboo shoot" seeing as the thing is bamboo
Hopefully that wasn't too much of a Japanese nerd out there