芸妓 is how to refer to a geisha that offers “special services.”

Please don't order this, it's only here for reference. 芸妓 is not appropriate for custom calligraphy!

In Japanese, 名妓 means “distinguished/talented/beautiful geisha.”

The meaning in Chinese (and the deeper meaning in Japanese) would be “distinguished/talented/beautiful prostitute.”

I am not sure that our master calligrapher will even write this, so please note that fact if you decide to place the order. Of course, we'll refund your money if he refuses.

玄人 literally means “Mysterious Person/Woman.”

In Japanese, this is associated with a “geisha,” which matches this definition of a “mysterious woman.” However, this is the colloquial way to say “professional geisha” or “expert prostitute” in Japanese. It, therefore, might not be what you want on your wall.

Notes: This is a "Japanese only" term, though a Chinese person who sees these characters will think of a geisha or an alluring Japanese female musician.
While not often seen in Korean Hanja, this would mean a "dark woman," as in a woman that you cannot easily see through.