What are people, male or female, working in a Brothel, called?

They sure are not called call girls or hookers (absolutely not!). I don't believe "call girls" because these are people working in an establishment, right there, not making calls, not that 'kind'. Prostitute is a general terms for all such people who sell their body for pleasure. Hooker is someone you Meet, I believe. So is there an actual terms for such service people? Gracitas

Solution 1:

"Sex workers" is the term used by licensed Social Workers, the medical community, women's (and men's) support groups, and the media when referring in an unbiased way to those who "sell their bodies for pleasure."

From Wikipedia:

"A sex worker is a person who is employed in the sex industry.[1][2] The term is used in reference to all those in all areas of the sex industry including those who provide direct sexual services as well as the staff of such industries."

See: https://en.wikipedia.org/wiki/Sex_worker for additional information.

Solution 2:

"Sex worker" is the term, but "brothel worker" is also used, not as broadly as sex worker, though.

The brothel worker: 'I regret not working in the sex trade as soon as I got here'

[Source: theguardian.com]

Missing Love Ranch brothel worker found safe; friends said she disappeared after Lamar Odom's hospitalization

[Source: nydailynews.com]

You can use "hooker", also (it is not absolutely wrong) as in the above linked article shows.

The Love Ranch hooker who partied with Lamar Odom then reportedly went missing has been found.