Assuming those are tho _only_ directories beneath `/tmp`:
$ find /tmp -mindepth 3 -type d -print | sed -e 's/\.[^/]*/./g' -e 's/^.* //' -e 's#/##g'
I.01.a.
II.03.d.
The `find` command finds the directories on level 3 and prints out their full path. The result of this step is
/tmp/(1) I. First Majuscule Roman Numeral/01. First Arabic Numeral/a. First Grapheme
/tmp/(2) II. Second Majuscule/03. Third Arabic/d. Fourth
The `sed` command does three things:
1. replaces everything from a dot up until the next slash with a dot, creating
/tmp/(1) I./01./a.
/tmp/(2) II./03./d.
2. removes the bit up until the first space,
I./01./a.
II./03./d.
3. removes the slashes,
I.01.a.
II.03.d.