I have been wondering the name of this tree for years; I really like it.

Also, what are some evergreen species that would look nice in a Japanese garden? (Traditional or not) I plan on making one in spring.

After doing some quick looking around it seems to be a Norfolk Island pine, which is sometimes also called star pine, triangle tree, or living Christmas tree (according to wikipedia). I know nothing about gardening though so I can't help you with your Japanese garden, sorry.

The picture isn't showing up for me. However, I can tell you that the best way to find out what works best for a Japanese inspired garden, is to look at them. To a little bit of digging about the historical and cultural significance of their horticulture. Chinese and Japanese gardens are much more than pretty plants, often they incorporate some sort of deeper meaning. One person who might be of value to you is a guy named Mirei Shigemori, a modern Japanese landscape architect. I believe he's no longer alive, but his work definitely broke boundaries in Japanese horticulture.

For more help, though, I've seen a lot of pines and azaleas in the Japanese-inspired gardens I've visited. It's also important to make sure the plants you purchase are actually suitable to the site! With more digging in that regard, you'll be able to find a more concrete answer.