Is it spelled hamam or hammam?
Both spellings appear in English. Hamam is the Turkish spelling; hammam is also widely used for bath traditions in other regions.

Related questions
Where does the Turkish hamam tradition come from?
It developed from earlier bathing traditions, including Roman baths, and took its own form in Ottoman society. Today's treatment packages are modern services, not an unchanged ancient ritual.
What happens on a first Turkish bath visit?
Usually you check in, change, warm up, receive the booked scrub and foam treatment, rinse and rest. Oil massage is a separate stage when included.
Which Turkish words are useful in a hamam?
“Daha hafif, lütfen” means “more gently, please”; “Dur, lütfen” means “stop, please”. You can also use simple English and a clear hand signal.