Yes and No. Taka is the real world version of Tamahome, but he lacks his memories and his powers. However, *SPOILER* he regains them towards the end of the manga.
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Taka is like the "real world's" version of Tamahome. Since Tamahome lives in a book called 'The Universe of the Four Gods'. Think of Taka as Tamahome or Tamahome's Reincarnation in the real world who's lives with Miaka in her world and remermbers her from "The Universe of the Four Gods" Book.
In the Anime and the Manga (if my memory is correct) Miaka pretty much ends up marrying Taka (who is the reincarnation of Tamahome from the book called 'The Universe of the Four Gods'.
In Fushigi Yuugi, Tamahome is Miaka's partner. Later on, since Miaka and Tamahome couldn't stay together in the same dimensions (Miaka had to go back to her dimension when she had fulfilled her role as priestess of Zuzaku and Tamahome didn't exist in her dimension and if stayed would disappear.), Miaka went back home, and Tamahome was reincarnated into Taka in her dimension so they could stay together (though had a little trouble at first finding each other). So now Taka is her partner.
TAKA
it also means honor