Does a small bathing alcove mean a private room?
No. An alcove can be part of a shared bathing area. Ask whether your booked room is enclosed and exclusive to your party.
Related questions
What is the difference between a private and a shared hamam?
Shared space may include other guests. Private use should specify which room is exclusive, for how long and whether changing or rest areas remain shared.
Can couples have a Turkish bath together?
Some venues offer arrangements for couples, but confirm that you will share the same treatment space and whether it is private. A booking for two alone does not guarantee either.
What does double hamam mean?
A double hamam has separate bathing sections traditionally arranged for men and women. Historic layout alone does not establish today's admission or staffing policy.