I am looking for an indigenous German word for women who entertained guests at social gatherings in Germany. To put it simply, I am looking for a German analogue of geisha.
Considering that the exaxt same concept of a Geisha does not exist in German (or, more generally, European culture), there is no such word. Concepts that come close and might be a more or less loose fit are
Hausdame - This denotes (or mainly, used to denote) the concept of a female member of (rich) households who took the social/entertainment obligations of the spouse of the head of the house when there was none or not able to take that task. She led the household's staff, entertained and looked after elderly members of the household and basically did everything that would have been expected from a female head of house (no sexual connotations here). A Hausdame would, on occasion, also have participated in social events just like the spouse of the head of the house would have. Those were long-time employed, unmarried women, not only hired for special occasions. Today, a Hausdame means head of staff in Hotels.
Gesellschafterin is a similar concept, but not based on long-term employment. Here, the concept is more based on entertaining guests and members of the household, without the other functions. The term Hostess used to have a similar meaning until it became mis-used as euphemism for escort-service. Silvia Sommerlath, today Queen of Sweden, used to work as Hostess at the Olympic Games where she met her husband.
The word you are looking for is:
It exists in German vocabulary as a foreign word.
The concept of a female entertainer at social gatherings does not exist in European culture. And so in the context of a conversation in German language, the word "Geisha" will be interpreted differently than in a conversation in Japanese language. In an European context, the word "Geisha" always has the connotation of an east-asien submissive sex-worker.
So, when you want to talk about Geishas in Europe, you first of all have to make explicitly clear, that you are talking about a feature of Japanese culture, that does not exist in Europe.
And be aware, that the idea of a female entertainer at social gatherings is considered to be political incorrect in Europe. It is sexistic in western culture.
Imagine a high-class social gathering
For such an event there would be one person to organize it. This person would invite people "with partners". The aim is to invite same count of men and women.
There are two possibilities how to solve a "men surplus".
1: Invited men can book an "escort girl"
They pay for a woman, who escort them to this event. (There are a lots of media, which paint the picture of "escort girls" like "first the event and then sex as bonus", but there have to be some respectable agencies as well). The men do not tell everyone about the booking I think. It is not such a well accepted or respectable thing compared to a geisha I think.
This women are called "escort girl" in German too, also "Begleitservice" and "Begleitagentur" are related words.
2: The organizing person invites extra women
The organizing person do the "invite with partner" and wait for answers. The host counts the men who come alone, and finds for everyone a woman, who he is familiar with, or have likewise interests, and additionally invites this. This is a very complex task. The successful accomplishment of this challenge is a commendation for the host. I can imagine, there are some women who are educated and have the "right background" who are invited very often to such events.
This is well accepted in traditionally context (where such events are used for unwed offspring to get in contact with "proper persons of opposite gender").
The concept here is "Tischdame". She is a guest also, but through the seating arrangement one woman is assigned to one man.