Reader Lori W. has sent me a jewelry website called DragonWeave. I was surprised to find this showcased in their Japanese/Chinese section:
The character shown 妓 does not mean "geisha" when it is just by itself alone.
妓 means "prostitute".
In Japanese and Chinese, "geisha" was originally referred to as 芸妓 and 艺妓. As in any language, the character 妓 has changed its meaning over the years. This is similar to how the English word "gay" has changed its meaning over the last several decades.
Today, 芸者 is used to represent "geisha", which means "person of the [performing] arts" or "art person".
In modern English, the term "geisha" does carry connotations of prostitution. This relates to the American occupation of Japan after World War II, when some young women, desperate for money and calling themselves "geisha," sold sexual favors to American troops.
The confusion between the geisha profession and prostitution has been complicated by Japanese prostitutes, particularly at onsen (hot spring), who wish to co-opt the prestige of the geisha image by marketing themselves to tourists (both Japanese and non-Japanese) as "geisha," and by depictions of geisha in Western popular culture, such as the novel and film Memoirs of a Geisha.