the current guidance notes make it clear that the British government expects dual nationals to change their foreign name to be the same as their British name, if they want a new British passport. From page 5 of the guidance notes: British passport Guidance_Notes 2017 .pdf
If you are a dual national, you should send us a full
colour photocopy of the uncancelled non-British
passport, or British Overseas Territories Citizen passport
(every page including blank pages). If you hold a non-
British passport in a different name, you must change it
to match the name you want on your British passport.
You must do this before you make your application.
The guidance notes also specify that dual nationals in the UK are not eligible to apply online. Applicants in Thailand, as we know, are required to make an appointment online and apply in person at the Trendy Building.