Bananame is a slur used to describe Asians in a derogatory way. "Banana" and "anime." Refers to Asians, esp. Filipinos, who are fixated on Japanese pop culture(anime, music, etc.), only date Japanese, try to be Japanese.
The word Bananame is a racial slur that has been used historically to degrade and dehumanize asians. The word is still used by some people for this purpose, and it is seen as offensive and hurtful to asians. If you are unsure about whether or not it is appropriate to use the word Bananame, it is best to err on the side of caution and avoid using it in any situation.