The purser said that the dragon's name was Mrs. Scrivener-Yapling, with a hyphen.
The hyphen is used between the component parts of some compound words.
The hyphen is used also when the words are inverted; as "four-and-thirty," "six-and-fortieth."
But if the word "part" or the word "share" follows, the hyphen is not used; as "two third parts."
There is no rule to distinguish ...