Discreet Lady,
you will choose your accountant carefully and tell them the complete truth about all your life. That way they can do the best for you and save you money on your tax bill by making sure you have claimed all of your expenses - anything you bought to use just for your business is and expense. Advertising. Travel costs. etc.
What you call it. Well I've never wanted sex worker on my records either.
Masseuse, holistic therapist, counsellor, trainer, life couch, dancer, trainer. This are all broadly possible and you can match up your expenses , travel and advertising costs to these business names.
The thing is in the future you apply for a mortgage, or a loan, or just to rent they will ask for your accountants info and they will phoe him or her to ask to confirm your income and what you do. So she/ he needs and answer - a job title.
Over the years ahead this is very useful. I have been with my accountant for 20 years and that alone carries some credit when you are applying for things.
You said you are running another business too. It will be the same accountant. They will put together your income and costs for both businesses separately and come up with your profit figure for both businesses. But then they get submitted on the same self assessment form.
If you are doing well they will advise you about when you should consider setting up a limited company (for tax purposes) and they will also advise you on VAT if you start to take so much money you are near that threshold.
You never want to be taking £80,000 per year from escort clients, because you do not want to be registered for VAT in this business, IMO.