I don't know how anime fans like this, but lots of people call them weeaboos. Don't ask me why, I didn't make it. Also... It sounds good after another stereotype. Like "Emo weeaboos". Good meaning so stupid sounding with anything else it's good and funny.
You can be an anime fan without being a weeaboo. That word (as derogatory as it is most times) generally means the same as "Japanophile" and extends to other things than purely anime. I've heard "otaku" is used for hardcore anime fans otherwise.
Otaku is the most common one. Otaku really means an extreme fascination in something to the point of being eccentric - a hardcore gamer or someone who plays chess all day could be considered an otaku, for example. But in the West "otaku" is often used to refer to people who really like anime.
Nakama means something else entirely. Nakama is the Japanese word for a friend you have such a strong relationship with that they can almost be considered family. Calling somebody "nakama" is basically like saying "I love you" in a totally platonic way.
"Otaku" to me implies a kind of obsessive devotion to and interest in something. "Weeaboo" implies a poser, a wannabe--someone who pretends to understand Japanese culture but doesn't. Neither of these words seem accurate to me to describe someone who is simply a fan of anime or interested in Japanese culture.