Put your cursor on the box and type
C-u C-x =
It will give more useful pointers. The codepoint of a particular
character. The name of the character, in the example below is prefixed
by the script it comes from etc.
Actually, the "name" first is just the official Unicode name of that
char, which is only indirectly linked to Emacs's (and fonts's) notion of
a script, from what I understand.
I suggest you M-x report-emacs-bug requesting a new feature that
displays (in C-x =) the charsets (and/or scripts) that the
current char belongs to.
Stefan