For example in the rhyme "Miss Susie" the end of each verse is linked to the next. Would these just be called puns? Or is there a more specific name when they are used in this way.
Miss Susie had a steamboat,
the steamboat had a bell.
Miss Susie went to heaven
and the steamboat went to Hell–
please give me number nine...
The first verse ends with "Hell" which is merged into "Hello" in the next.