Is there a Fujita in Japan?

Yes. Fujiwara is an aristocratic family in Japan, and most of the surnames including Fujiwara are separated from Fujiwara. Because Fujiwara is one of the four big noble in Japan, there are many families, so there are many Japanese surnamed Fujiwara. Of course, some people take some surnames with rattan characters in order to stick to Fujiwara's surnames.

The surname related to Fujiwara is "Sixteen Rattan", namely:

Sato, Ito, Saito, Kato, Goto, Kondo, Endo, Kudo, Ando, Naito, Sudo, Wu Teng, Fujito, Omo, Shen Teng, Haruki (in population order, Sato is also the largest surname in Japan).

In addition to "sixteen vines", there are also

Jiangteng, Zaiteng, Kanto, Jiteng, Banteng, Haiteng, Shouteng, etc. ...

Common surnames beginning with rattan include:

Vines, vines, vines, vines, vines, vines, vines, vines, vines, vines, vines, vines, vines, vines, vines, vines, vines, vines, vines, vines, vines, vines, vines, vines.