Got it at last.
My browser normally allows web pages to select the fonts that they render text in rather than have the browser's own default font (e.g. DejaVu) applied.
AAM has messages fonted according to this CSS rule:
font-family: 'Segoe UI','Helvetica Neue',Helvetica,Roboto,Oxygen,Ubuntu,Cantarell,'Fira Sans','Droid Sans',sans-serif;
Whichever one of this list the font applies, that one must have some error in it.
Now, having unchecked the option in my Firefox settings to allow web pages to select their own fonts, I can see Páid's name rendering correctly. Likewise with é, ç and û on the French keyboard and ö,ä and ü on the German keyboard.
Tá brón orm nach rinne mé cuid mó scrúdú faoi na rudaí sin sula chuireas ceist chuig AAM orthu.