THE WORD GEISHA = GEI SHA 芸 者 (GEIKO is a Kyoto term for a GEISHA. Same thing. Six of one, Half a dozen of another). The first character GEI 芸 is usually translated into English as Art, or the Arts. The second character SHA 者 simply means Person. Together they mean A person of the Arts. Therefore......ARTIST. That's simple enough. But, sculptors, painters and potters are also "people of the arts". May we call them "Geisha" as well? No.
The two Chinese characters for GEISHA are specifically reserved for the women in this so-named Geisha profession who have been trained from childhood in the Performing Arts such as Music, Dance, Speaking, or Singing for the purpose of entertaining others in venues clearly defined for them.
ENTERTAINERS is probably a better translation of the word, but that, too, is far from sufficient, and is more likely to conjure up images of Stand-up comedians or Lounge Singers in a Las Vegas Night Club act. Besides, there is already a general Japanese word for TV Personalities and "entertainers" in this category : 芸 能 人 GEI NOH JIN.(Notice that the first part of that word also uses the same 芸 GEI character used in GEISHA).
Actually, there is no good English equivalent for 芸 者, as the Geisha is purely a Japanese phenomena. Not even their neighbors, Korea and China came up with the exact same thing. Thus, it is simply better to use the word Geisha, and simply know what the word entails when you are talking about her.
The photographs are beautiful and capture a culture and time I think many of us know little about. You can read more about Geishas here.