Should proper nouns be transcribed with Esperanto letters or not?
For example, for Gia, should I write Ĝia, Ĝiao, Giao or Gia?
The tradition within UEA is to transscribe the names of towns where UKs are held. Also the names of famous esperantists are usually transcribed or they have taken an Esperanto name.
I would say that for others, it depends. The more pronunciation differs from the Esperanto pronunciation, the better is the idea to transcribe.
Take for instance the Italian esperantist Gian Carlo Fighiera. If he does not have an Esperanto name, you can write "Gian" and provide a pronunciation hint, e.g. "Gian [Ĝian]". Or you can fully go with the transcribed version using a stipulative introduction "Gian, poste en formo Ĝian laŭ elparolado". But it really depends on the situation.
Names written in non-Latin-based writing systems, for instance the former emperor 嘉靖, are always latinized into form that follows pronunciation, so Ĝiaĝing. Here you can use an introduction like "Ĝiaĝing (ĉine 嘉靖, piĝine: Jiājng)" like they have done in Wikipedia.
Historically there was a tendency (idealism) to Esperantize names, and in case of say the bible it was apt and unavoidable.
Nowadays a more modest approach is to let the latin names as they are (and also not accusativized): Gia. Following the transcription of non-latin scripts I think non-misforming accents are possible: Ĝia. Especially where the pronunciation is probably unfamiliar to the reader. Ĝon for John forms a secret language. Or better (as possible for all names) make a footnote of the phonetic pronunciation. Anything else would have needed a footnote for the original name!
Only in settings without couleur locale, like in a school play, a short story in any city, one might consider invented, hence Esperanto names, where Johano might be more appealing than Johannes or better prononciable.
Geographic names are a bit more Esperantized, though not for village level names. This is not uncommon in other languages: Liège/Luik/Lüttich, Aachen/Aken, Nijmegen/Nimwegen.