I did this just a couple weeks ago. We're doing an author study on Audrey Wood, so I read them the book "Silly Sally" Now, the book doesn't really have any alliterations in it besides the short phrase "Silly Sally" but I showed them how the first letters of those words had the same beginning sound and we made it into a longer sentence. "Silly Sally Sung a Silly Song" and then we made up ones with our name. I told them they might try brainstorming words that started with the same letter as their name and look some more up in the dictionary because some had a hard time thinking of words that started with a particular letter.
I know another teacher that did it with the same thing, except with the book "Wemberly Worried" by Kevin Henkes